Good luck Seiya! Have fun
I'd love an update afterwards as well

I'm not sure if you are most concerned about his social anxiety level or just the red flags in general.

first thing, lately for myself I think I would rather find a more introverted female, as I am an introvert and somewhat non-social. I have been with (all of my mates) only extroverted females and not one of them worked out. for me, I don't think the old addage "opposites attract" works. So in a general sense, answering your question about social anxiety, I don't think it would necessarily be bad.

The problem occurs with the fact that he seems to be overly concerned about it and only time will tell if that's a real issue, but that it makes you uncomfortable should say something, at the very least, to tread carefully in this relationship.

The issue with religion is probably a bigger one IMO. Simply because belief systems tend to guide people in everything they do and although I quote the bible on this, the principle is true that being "equally yoked" is a very good thing. That is, being from the same perspective on your beliefs. If anything is a real red flag, it's this, but that's only based on your framing of his belief system contradicting yours. It may not be an issue but again, I think you need to explore this a bit more before commiting to anything serious.