One of my guests is brining a picky eater with her and I refuse to alter the menu for them.
Have you brought this up with your guest and found a compromise about it?
It's my dinner party and my rules.
I get that you don't want to change the food for your party but it would be really rude not to try to accommodate the picky eater at least a little. You were given the information you needed to do so, so you should try to be a little flexible and adjust plans a bit for them.
Well since you make it sound like i'll be a bad person for not compromising, maybe i'll find something simple for them to eat.
I am not making you sound a bad person, as that picky eater is the one that is causing the problem for you with your event, and unless they have a medical condition, I think they are the ones in the wrong. But to be a good friend and to accommodate everyone, compromising with the food choices is still the better thing to do so that they would appreciate your effort and enjoy themselves there.