I have to say, she is right in that you both need to have outside activities, time to yourselves, and/or your own time to spend as you wish. The problem is that most people associate bars and clubs with being single and rightfully so. On the other hand, it really is a matter of trust. Do you trust her to go out and not cheat. Now keep in mind, I didn't say go out to the club, I said go out. Go to the store, work, park, club, her families, the beach, shoe shopping, food shopping, etc. Because the fact of the matter is, people are either cheaters, or they're not. If they are a cheater, they don't need to go to a club to find someone.
If you decided to go to the club with your friends, the only way that it would be disrespecting her is if you cheated on her or acted in any way that you would not act if she was standing right there. Keep in mind that it's possible that her experiences going out with friends may be different than your experiences. For example, the mindset that you and your friends (as men) went out with (ie; meet women, flirt, drink, bed women) may not necessarily be the mindset that her and her friends are in when they go out (ie; relax, talk to friends, have a drink, dance, have fun). A lot may have to do with your differing perceptions of what you get out of going to the club.
I don't know how long you've been dating, I'm assuming if you are engaged that you have been involved for far longer and know her very well. Well enough that you trust her and want to marry her. If you don't trust her then you want to rethink you're marriage plans and put more effort into getting to know her better.
If her going to the club is a dealbreaker to you, meaning you just will not stand for it, then you have to let her know that, but it doesn't necessarily mean that she will agree to stop. You will have to try and compromise with her and see if you can come up with a plan that you both can live with
I welcome your thoughts, let me know if you want to talk more