Personally, I wouldn't put up with it. Not only does it go against the idea of being faithful, but it's also unsafe for both of you (him having sex with random girls and then coming home and having sex with you). I've HEARD of other people agreeing to it, but nobody I know, and I'd never agree to it, but it's up to you.
But it sounds to me like your husband may have a sex addiction. You mentioned sex with no strings attached, and if those are his words, then it sounds to me like he's after either the sex or the game...not love. You didn't describe any other sign of him not loving you...that's why it sounds like some sort of addiction or maybe even a mental "macho" problem.
I would recommend going to see a marriage counselor, which in turn, may lead to some personal psychological help and advice for your husband. It will help determine whether it's he's a sex addict or has a ego problem, or if it really is a factor of him not loving you anymore. But you can't force him to do it. If he refuses to go or ends up showing no effort, then you may be facing the possibility of divorce...unless of course you decide to give in to his request.