at first my opinion was, if she wants to cheat, she'll cheat regardless. but after i read a couple of posts, i kinda see the other side aswell. You may trust your girl but if she cheats on you, chances are your ego will hurt not because she cheated but because the dude she cheated with feels like he got one over you and that's what hurts the most. the fact that you look like a fool. and so again, if you trust your girl and she gets a ride home from some other dude who thinks he could fuck, in his mind he thinks that you're a sucker cause he could fuck your girl without you knowing if he wanted to (again that's strictly his perspective). and if other people see that, they'll also think you're a sucker. so in a way, yes it's a matter of repect and ego and insecurity. except in this case, the insecurity doesn't stem from the possibility that she may cheat but rather from what the other guy and your friends may think regardless of the fact that in your mind she's most likely not cheating.
EDIT: bottom line, i understand why people might have a problem with it. we all have egos. we all have certain insecurities. and everyone has a different standard as far as what challenges their ego/plays on their insecurities. i think it's really case by case and you have to be reasonable. sometimes you should compromise and sometimes you shouldn't but there is no definite answer.