What is the opinion on Residents Association? Is the word "Residents" possessive or adjectival? My opinion is that is adjectival (as in the similar Community Association) rather than possessive. I.e. it consists of residents rather than belonging to residents.
As presented, Residents is adjectival, a common choice in this situation. The possessive forms are Resident's (singular) (but presumably there is more than one resident in the association, although it could be used as an exemplar: cf. Reader's Digest) and Residents' (plural). Sometimes the possessive in this situation is viewed as being too fussy, hence the adjectival use.
So do you think "Brighton Residents Association" is preferred over "Brighton Residents' Association" (for example)? A search of the internet shows both forms, fairly equally spread. To my eye the apostrophe looks wrong, for the reasons I stated above but a colleague insists the apostrophe is correct (but then he always puts an apostrophe when he uses the word 'phone and never uses the final "s" in "Nicholas's"!)
So do you think "Brighton Residents Association" is preferred over "Brighton Residents' Association" (for example)? [...]
Each is preferred by some people; neither is incorrect. It's a matter of style.
If a body registers its name with the apostrophe (no matter the rights or wrongs of their chosen style) then that's how it must be represented. Likewise, if the registered form of the name is apostropheless, its rendering must always be thus.
It's commonplace for business and organisational names to not employ the apostrophe.
To misrepresent a person's or body's name is ignorant (in both senses) -- an example being somebody's writing Wicks for Wyckes.
"Style is knowing who you are, what you want to say, and not giving a damn." — Gore Vidal