Many aircraft carry microwaves. But, every piece of equiptment is approved, in AA's case by the FAA, and considers emissions and interference and the means undertaken to minimize those.

But, the food safety concern has to do with mixing food not prepared to AA's standards with its own food. Some FA's may still help out and figure out a way to warm something, but they should not.

If you are unable to eat what is offered, you should plan on bringing food which is properly eaten unheated.

Not sure why a vegetarian would be flagged on a No Fly List merely for food choice.