My girlfriend and I have different religious beliefs...and my anxiety can't handle it

First off, I've had various forms of anxiety for most of my life. I just had a bit better control over them until recently...

So, I'm agnostic, and my girlfriend is converting to Judaism. I've known her for a year and half, and she's been converting for all of that time, so it's not like this is a new thing. I have absolutely nothing against Jewish people. That being said, I was mostly raised without religion, and what exposure I did have to religion turned me off of it. In the beginning of our relationship, it wasn't really a big deal, but as we became more serious and started talking about our future together, my anxiety ramped up.

At first, I was mostly anxious because I was worried we wouldn't be able to figure out how to make this work and eventually she'd realize it would be easier to be with a Jewish girl. The solution to this was for me to attend some Shabbat dinners and a service or two. At these dinners, though, I felt so out of place and my social anxiety was cranked up, because I felt like a complete outsider. At a later dinner, someone she didn't know well who was there mentioned that they didn't approve of interfaith marriage. My girlfriend promises this is not how the people she hangs out with think, but my mind can't get over it.

Now, my mind has latched onto our future children. She wants to raise them Jewish. When I'm thinking soundly, I'm fine with this. I'm even on board with it. When my anxiety kicks in, I worry I'm going to spend my whole life alienated from my children and with very little control over their lives.

This is literally the only issue with our relationship, but it's becoming consuming for me. When we're together, I feel safe. We get along great. We have similar goals and values in life. But every time I worry, I get this overwhelming urge to flee. I don't even particularly understand my feelings, because logically, I am fine with all of the above. I like learning about new cultures. I see nothing wrong with us having a kid raised in a Jewish community, as long as they know they have options for other religions if they wish. I know Judaism is something that makes my girlfriend happy, and I want her to be happy. BUT my anxiety apparently does not want her to be happy.

I'm at a loss, but this is becoming a big problem for me. When I'm alone with no major distractions, (such as on the bus everyday), it's the only thing I can think about. Then, I end up obsessing over little things, like I ended up reading about circumcision yesterday for a half hour and trying to decide how I felt about it.

This is the girl I really would like to marry, but lately I've felt like I'm just not strong enough to sit back, be chill, and stop worrying her entire community secretly hates me, and that I'm ruining her connection to this community she's built for herself. (Yes, she does say that's not the case.)

I just...need insight and advice. What can I do to help myself worry less? Why does this even freak me out so much in the first place?? What can I do when the urge to flee comes over me? I really want to make this one work, but I'm pretty sure my anxiety does not.

Thank you.