These are all very easy to discuss at work without politics. You ask, "Do you have any dietary restrictions? If so you should make sure to read the menu closely, it'll tell you what the dish contains."

There, now I know as much as I need to about my coworker's diet. We're here to work and if you're going to be a member of a _diverse_ community with a shared goal you're going to need to accept that other people live their lives differently than yours and that's ok. I don't need to know the reason my coworker is a vegetarian I just need to let them know if my cookies that I brought to work contain animal products.

If you refuse to get along the result will be internal strife and the shared goal, a successful company, a working community, etc. will fail.