This is going to sound rather harsh but I want you to remember, these are invitations. You are welcome then to eat at their places. Try to look at it this way: as hosts that have invited you over for the night they actually have an obligation to feed you. Now, you don't have to eat everything put in front of you. You might choose instead to nibble. This way you are still showing respect. Incidentally, in my opinion, the fact that they have repeatedly made the offers to you indicates they are sincere. I have used the term respect - as they should respect your own decision, realise that they ought to be shown some respect in return. What I am saying is that they actually might be having their feelings hurt. To be honest, if I were to entertain someone and they appeared to turn their noses up at my offer of food, I would feel more than a little hurt and put off - even more so if they brought their own food. What kind of message might you thus inadvertently be sending?

I realise this is a difficulty for you but I suggest you try to look at this from the others' points of view.

A solution to these situations is to get involved. Offer to help make the meal. Could doing so be a way then of easing your anxiety about consuming it?

Finally, I am wondering about your relationship with food in general. Has something in your past spurred this worry about consuming other people's food? Is there a reason you tell yourself you are not allowed to? I think this would be an excellent point to bring up with a therapist.