In my experience, the man who has a problem with you "going Greek" is also likely to have a problem with you joining the marching band, a service organization or anything that takes time away from him. This may occur whether or not he's Greek himself.
That said, there are also those who have an issue for whatever reason with Greek life in general. If you're in a close relationship though, they should respect your judgement once you explain why you are interested.
To answer your question, yes, I have seen others (and at one point, myself) become less or inactive because they had a critical significant other.