“User's guide” vs. “users' guide”
I prefer non-possessive form of the name of the club: photographers club of Detroit. Is it correct?
No one can object to Detroit Photographers’ Club. A club has more than one member and that is shown by placing the apostrophe after the s. However, this is one instance where the apostrophe is disappearing: nothing is lost by omitting it altogether.
According to ‘The Cambridge Guide to English Usage’, the removal of the apostrophe from 'plural nouns in phrases which express affiliation . . . is widespread in the English-speaking world' and has the imprimatur of the American Associated Press stylebook and the Australian government Style Manual. As the Cambridge Guide says, ‘the time spent worrying about whether it should really be driver’s licence or drivers’ licence would be better used elsewhere.’
It depends on the word photographers. If it's a modifier not a pronoun then you don't need an apostrophe. In which case, I don't think you really need the plural form of it. So it should read:
Photographer club of Detroit.
However, if the word photographers acts as a possessive pronoun, then you need an apostrophe.
Photographers' club of Detroit. Or Photographer's club of Detroit.