I'm currently in a similar situation. I'm Asian(female), but my bf isn't. I /have/ to hide him too and will only let my parents know when my parents start pushing me to get married in a few years. it definitely does have an influence on the relationship.

From what you've said, it does sound like it sucks a great deal and the status quo does really suck. I would personally say it's more to do with culture rather than religion unless you have different religious backgrounds? Do you think his family will disagree if they knew about you? I'massuming he's from a conservative family by reading what you've written? If so, I can understand the struggle and the fear of telling your family about it as having relationships before marriage frowned upon. It's not as easy as just telling them no if they disagree which sucks as it can mess up the family.

As always the choice is ultimately yours, you have said it's tiring and emotionally draining, it depends how much you're willing to continue with it if it really is taking a toll as it isn't healthy. On the other hand, you have said it's roughly a month or two till he can tell them. You can wait till then, but think about what if something else comes up and delays him telling them even more so? My main piece of advice would be to get it out of him if he does 100% want to tell them and have a discussion of the realistic (possible) outcomes there could be so that both are ready for anything. If you feel like it's too much right now, walk away. If you want to wait then do so as there's nothing wrong with it. Bear in mind, if he keeps pushing it forward then reconsider what you want to do.