This is a problem for us too as DS and I don't like eggs. That's why I haven't booked the breakfast with Stitch, although we LOVE Stitch. DH on the other hand would be happy to swim in a big bowl of scrambled eggs.
As I stated earlier....
they also serve breakfast potatoes, mickey waffles, various Hawaiin breads and rolls, sausages and bacon. It is not just eggs. Everything was really pretty good.
I highly suggest you give it a try. The character interaction was great. When we wanted more they were more than happy to bring out more of what we requested