Your first example without the apostrophe is correct.
Nouns are marked as possessive by either 's (Ed's car) or in the case of plural nouns ending in "s" with just an apostrophe alone (the girls' dormitory).
So when we look at the phrase "Beatles fan", it's tempting to see the "s" on the end as possessive and add an apostrophe to give "Beatles' fan".
But that would be a mistake because in fact the "s" on the end is there to mark the word as plural (there were 4 Beatles, I recall), NOT as possessive, so no apostrophe is actually required.
We can prove that by taking another pop group whose name does not end in "s" and seeing what happens. "Queen" will do:
(1) A Queen fan
(2) *A Queen' fan (wrong)
(3) A Beatles fan
(4) *A Beatles' fan (wrong)
In (2) an apostrophe would be ridiculous, so (1) must be correct. And the same applies with the other pair - (3) must be correct.
Your example in full was "Beatles fan conventions", and the same applies:
(5) Queen fan conventions
(6)*Queen' fan conventions (wrong)
(7) Beatles fan conventions
(8)*Beatles' fan conventions (wrong)
Thank-you, that all makes perfect sense. I thought that it was the sentence without the apostrophe, but I just wanted you to confirm it.
It has been a real eye-opener for me whilst using this forum. I have realised just how little I know about my own language. I think it was Nietzsche who wrote about people who rush to learn foreign languages and yet haven't even mastered their own.
As I am composing the text for plaques that the public will read, I am challenging every grammatical problem that I come across, no matter how small.
The next plaque should be hung this week. I will make sure that you and your forum get a mention in the local newspaper and on social media sites.