Proper nouns in general are not an issue. But let me ask about a proper noun that is a generic group name, so as to then involve its members. I'll give two examples, The Beatles (a pop group containing 4 people) and Evergreen Trees (a group that includes all trees that do not shed all their leaves at the same time).
As proper nouns, both group names are capitalised: The Beatles; Evergreen Trees.
Both are singular items (that's why they are proper nouns): there is only one group called The Beatles and only one group of Evergreen Trees (so each s is, at best, just idiomatic and does not literally describe the presence of plurality)
What about the members though (this is where my question focuses)? It is easy to locate reference to "a Beatle" (note capital letter and absent s) but very difficult to locate a reference to "a beatle". Ringo Starr was "a Beatle", why not "a beatle"? Ringo Starr was not the only "Beatle" ("beatle"?), George Harrison was a Beatle (or should it be "beatle") too, so as there were 2 Beatles (/"beatles")(or even actually 4) a beatle cannot be a proper noun so shouldn't have a leading capital. So why is Beatle not written as beatle?
A member of the Evergreen Trees is an evergreen tree, not an Evergreen Tree - or is this wrong? If not wrong, why are Beatle and evergreen tree treated differently?
The Beatles is a proper name because it is unique to that particular band, just like The Rolling Stones, and The Bee Gees . But "evergreen trees" is not a unique horticultural name any more than "deciduous shrubs" or "bedding plants" is. "Trees", "shrubs" and "plants" are just common nouns with a modifying adjective or another common noun plonked in front of them.
In writing, you can call Ringo Starr a "Beatle", Mick Jagger a "Stone" and Barry Gibb a "Bee Gee" since they were each a member of a group whose name was proper name. But if you wrote Mick Jagger was a "stone" (no capital) that would have a different meaning, and if you wrote that Ringo Starr was a "beatle", that might imply that he was a creepy-crawly! It simply makes no sense not to capitalise "Beatle", "Stone" and "Bee Gee".
Of course, it only works for members of groups with a plural proper name. You can’t say, for instance, that Roger Daltrey was a "Who" or that Freddie Mercury was a "Queen" (or maybe you could!!!).