California has outlawed so-called ex-gay conversion therapy. Social conservatives who might want to express outrage at this law need to make sure they're going to be consistent with their own views on other matters. Also, surprising as it may be to some, there are reasons for those with more liberal views on these matters to worry about a law like this.
I'll start with the second point. Those who recognize homosexuality as a social construction should at least be open to a worry about this law. Most experts nowadays consider our notion of being gay as socially constructed. There have been different ways of conceiving of people with same-sex desires over history. In ancient Greece, for example, it was relatively accepted for older men to favor a sexual relationship with boys over that of their wives, not because they had some notion of people who have an orientation toward people of the same sex but because they didn't think they could have as deep an intellectual relationship with women, and they thought relationships that we would now count as pedophilia were a deeper form of love because they could involve intellectual conversations.
We now have a notion that there's a phenomenon called homosexuality, where a small minority among the population has sexual desires for people of their own sex rather than for people of the opposite sex. But most people recognize now, whether they approve of such desires or not, that it's more complicated than that. There are people who have both kinds of desires, relatively in equal proportion. There are people who have more one than the other. There are people who have one predominant at one time in their life but move to a point at another time where it's the other way around. There are people who move toward same-sex sexual interaction primarily for political purposes rather than because of some already-existing inner state of being primarily attracted along same-sex lines. But our social narrative primarily divides human beings into the binary of gay and straight, with some allowance for bisexual when we're feeling a desire for more precision. The variety isn't remotely captured by that, never mind the phenomenon of trans-sexuality, and the idea that being in one of the two categories of the binary is simply a matter of how someone was born isn't exactly borne out by science, even if there is some evidence that the underlying state of how one's desires are directly can be partially influenced by genetic factors.
Many on the left on these issues push for alternative conceptions of homosexuality, including allowing those who see their same-sex attraction in a way that resists being considered gay in the usual sense, and if same-sex attraction is much more complex than just being straight or gay, as many who might be inclined to favor a law like this might think, then shouldn't we be interested in allowing therapists to encourage moving away from the homo/hetero binary? But it seems to me that this law might ban therapists from doing that, because it would be helping move someone with same-sex attraction away from thinking of themselves as gay. Many on the left on these issues should see that as highly problematic.
It's less surprising to many to see social conservatives resisting a law like this, but such resistance isn't as easy to formulate as it sounds, because the grounds for it might conflict with other conservative views. For example, if we don't have a right to health insurance covering exactly the things we think are medically necessary, then we don't have a right to health insurance covering a particular therapy that we happen to want covered. If we don't have a right to doctors performing a particular procedure that we happen to want performed, then we don't have a right to this therapy if we want it.
That being said, conservatives can consistently hold that the government shouldn't interfere with what private counselors can do, even if what they want to do is disapproved of by the main professional organization. But most people do think medical services can be licensed, and certain things done by doctors can make them lose their license. So this is, at least in principle, something that is within the government's traditional range of control. But I'd have to see the law, because if the guy NPR had on opposing it is correct then it sounds like they outlawed a good deal more than what careful study has shown to be both ineffective and psychologically harmful (i.e. the conversion therapy itself) and will not even allow a therapist to help someone who has unwanted same-sex desires to live a life that avoids what they see as sinful and unwanted (which is not remotely the same as converting them away from a sexual orientation). I'm not sure there's any scientific ground for taking it to be harmful to choose a celibate life over fulfilling one's sexual desires, and therefore the normal licensing standards shouldn't require it to be banned.
There may also be a religious issue. They did apparently include a religious exemption. But not exactly. They included an exemption for counselors who are practicing religious officials of some sort but who are not licensed counselors. A pastor, priest, or other religious leader who happens to counsel is exempt. But a nun working as a licensed counselor in a more medically-oriented psychological practice is not exempt. And a licensed counselor operating a business not being run as a religious non-profit is not exempt. Is this a violation of free exercise? I suspect it is, at least in terms of the aspects that are banned that aren't demonstrated as harmful (such as helping someone to find a counselor who can help them live a celibate life or referring them to a therapist who will encourage them to think outside the gay/straight binary or allow them to think of themselves in a way that is more about having same-sex desires than about belonging to some supposedly-scientific category of being gay, which really involves more politically than many think, and someone who opposes those politics but does have same-sex desires may well not be gay in every sense). Again, this is assuming the opponent of the law on NPR represented it accurately, but the state senator who supported the bill on that show didn't offer any correction on the matter.
There's also the issue of viewpoint-neutral endorsement. This is another place where conservatives will have a harder time making their case. They tend to think there's no problem with the government or government employees endorsing statements of religious content, because the establishment clause only prohibits the setting up of an official government-run religion, and many conservatives don't even think this applies to states. After all, several states had official religions when they entered the union. So it's going to be hard to press this argument if you hold that sort of view on the establishment clause. You might, however, make an argument involving inconsistency among those who do think it's unconstitutional for the state to endorse religious content (or rule out religious content). And you might easily make the argument on policy grounds, rather than as a constitutional problem that courts can then deal with.
On the consistency issue, I think there's some case to be made, but it's because there's already serious inconsistency. If we take seriously the prohibition of even mentioning classic philosophical arguments like design arguments in a science classroom, on the ground that it's somehow endorsement of religion, then we already are banning lots of stuff that isn't remotely religion. Because the design argument need depend in no way on any controversial religious premise, it's not as if someone who endorses such an argument has to be following any religion at all. It could be a purely secular theist who endorses a design argument. And merely teaching the argument, rather than endorsing it, is certainly not endorsement of religion. So those who claim that that's importing religion into the science classroom have such a broad view of what counts as religion that it might well be very hard to see this law as not endorsing a claim that speaks to a religious issue. It's on such grounds that a federal court has ruled that it's unconstitutional to present the arguments against intelligent design in a state-run science classroom, because it took that to violate the establishment clause.
But a much more reasonable position would be that intelligent design is not necessarily religion, even if it's also not strictly speaking science (although I would argue, and have argued, that it's not any less science than the metaphysics that commonly gets done by physicists working on cosmology, quantum-theory, and space-time). Someone who holds this more reasonable position might nonetheless not hold the conservative view on the establishment clause and therefore think that President Obama shouldn't be invoking God the way he does or that it's unconstitutional to endorse actual religious content in a public school science classroom, such as endorsing six-day creationism because the Bible teaches it. On that sort of view, it's still easy to present an unconstitutionality argument for this law. After all, the legal issues are the same as the above cases, but without the ridiculous claim that philosophical arguments are somehow automatically religious just because a lot of religious people accept them (which would make most of our beliefs religious). Then all you need to do is recognize that the value of at least some of the therapy falling under this broad ban is both (1) not as clearly harmful as some of the therapy it bans and (2) something religious people can endorse because of their religion. In that case, the government is not remaining viewpoint-neutral on a religious matter without the strong argument that the therapy is harmful.
And even someone who does hold the conservative view on the establishment clause (or who isn't willing to argue a case base on existing but wrongly-decided precedent) can give a policy argument against this at the legislative level. It's not unconstitutional, on this view, but it's compatible with that to think that as a policy matter the government should remain viewpoint-neutral on controversial matters of religious disagreement that aren't demonstrably harmful the way medical professionals do take ex-gay therapy proper to be demonstrably harmful. The result is that this is just poor policy and should be opposed as bad law. And that's something that someone pretty far on the left on same-sex issues should be all right with. The government shouldn't tell us what to think about such matters, and it shouldn't stop us from getting counseling that fits with what sort of life we want for ourselves, and if a minor happens to want this sort of therapy it shouldn't be illegal for a counselor who is willing to do it or to refer someone to someone who will out of respect for the client's wishes as long as it isn't one of those demonstrably-harmful methods that the ban doesn't limit itself to.
So I think a lot of the conservative arguments against this ban need to be very carefully done to succeed, but I think there are arguments, and some of them might appeal to those more toward the left. But those are more against the law as it stands, rather than against a different ban that could have been enacted. I do think there are real tensions on the left in how these issues are thought of, and I'm not sure it's as easy to justify this broad a ban as I assume many on the left would think.