I think what I'd do depends a bit on the belief itself.

If I walked into a Ts office for the first time and had reason to assume they don't believe in science, I couldn't work with them. There's certain things that for me we just have to agree on.

Then, there's situations that are more murky. I myself am currently in a kind of similar discussion with my T. My T thinks I should report an abuser who mistreated me years ago. I don't want to, because not only would it bring up a lot of old stuff and I don't think the abuser is a threat to anyone else, but also because I can't really feel that it was abuse. We have discussed this disagreement at lengths yesterday, because even though I can't tell yet whether there's also core beliefs about myself and the things you described in your post, if he disagrees with me it feels threatening to our relationship somehow.

One thing that certainly helps me is imagining somebody completely different going through everything I have. Not only that one situation that the belief is rooted in, but the whole thing leading up to it, from birth. Then, I think about whether I'd judge this person the same way, would I think they are bad, or that they were not abused, or that they were the best person in the whole wide world (this being kind of the opposite scenario where instead of devaluing everything I might idealize somebody way too much)?
For most people, they are not all good or all bad. I've done bad things, my abusers have done good things (even for me), my T always makes sure to point out he's also done bad things in the past... This usually shapes our perception of others, if I see my friend be kind and understanding 99% of the time but this one time he got really angry and lashed out at somebody for no reason, this doesn't mean I think he's always a bad person who can't do any good.

However, for me sometimes I only see one of the two sides. Taking my situation as an example, since my abuser was oftentimes good to me and I somehow managed to repress the anger about the abuse, I still see this person as a mostly good person and in my mind, I'd not want to have them arrested and in prison. Yet, if I imagine the exact same thing happening to a friend of mine and them telling me about it, I'd not see that abuser as a good person at all, nor would I agree with not reporting them, and I'd probably also express these opinions.

Thoughts like this don't help me necessarily feel any different, but it helps understand the other side. There's certain exceptions, when maybe your T is really just way off about their opinion and feelings, which is of course important to consider. But not only do I think that it's probably not the case with L, I also think that even then you'd have to think about possible counter-transference and all that, it wouldn't immediately be a bad thing.

Now, maybe talk to L about this if you can? Not the content of the disagreement, but the fact that you're struggling with the two of you disagreeing? My T said yesterday that having different opinions about topics and expressing that is good. It doesn't mean there's no overlap in agreeing on things at all, but it would be very exceptional to agree on everything. If the other person expresses an opinion different to yours, that doesn't have to mean that there's this huge separation between you and you disagree on everything, it can also mean that you can trust this other person, because they tell you how they feel about something, yet respect your own view of it and are willing to explore that with you.

He also told me to make sure to address it if I feel I disagree about something he said, it's a good way to learn from each other. If others just always agree with what you're saying, you don't consider new angles to things.