I want to start playing trombone will the trombone embouchure affect my saxophone embouchure ?

Unfortunately, the saxophone and clarinet embouchures use the opposite muscles required to play a brass instrument. So yes, playing trombone will affect your sax embouchure, but only if you let it. I'm sure that by being aware of the situation, you can help the problem. Make sure you always warm-up and warm down on each inst. Playing cold is never good, but it can be especially harmful when changing horns. So, you can do that, just be careful, but if you REALLY want to be serious about one of them, I wouldn't suggest trying to double.

yes it will mess it up good but that doesnt mean you cant get used to it. its just never gonna be easy

It will effect you sax embouchure, if you let it. Playing a brass intrument is different in the sense that it take constant maintainence. Saxophone isnt so tedious because there is a lot less effort used to play the instrument. You have to practice both. Its like working out. You just dont work out one bicep or one tricep, you workout you entire body, but not all at the same time.

Practice trombone more than you would sax because a brass embouchure is more likely to fall off than a woodwind. All it needs is practice. Practice doesnt make perfect, its make permenant.

Of course, in my personal opinion, your embouchure effects your tone/sound, to me I listen more for what you play rather than how pretty it sounds, kinda like a girl with an ugly face with a bangin body or a butt ugly girl with 30 million dollars. I like ugly.

Nonsense - do not believe everything you are told! Your embouchure for saxophone is totally different than brass embouchure. The only possible effect might be fatigue if you are playing both at the same show.

Numerous jazz musicians have doubled on brass, Benny Carter most notably (Alto Sax and Trumpet). Howard Johnson plays tuba and baritone sax, Tom 'Bones' Malone plays trombone and tenor sax, even Maynard Ferguson was known to fiddle occasionally on a soprano sax.

There would be great benefit to playing trombone and sax, especially in a jazz combo. Go for it!!