Many (!) dictionaries label 'many' a pronoun in such sentences as 'Many of my friends are grammarians'.
Yes, that's true. But dictionaries are fine for meanings, not for grammar. For example, they cannot handle the word class/function distinction, and they are not exactly greased lightning when it comes to adopting changes and additions. For example, expect dictionaries to extend the word class 'determiner' to the independent use of words like "many" in… oh, about fifty years or so.
Incidentally, for the uninitiated, the reason that independent "many" is best classed as a determinative (as opposed to a pronoun) is because it functions as a fused determiner-head. Thus, in a partitive construction like the one in your example, "many" combines (or fuses) the determiner and head, and is followed by the partitive complement "of my friends". We understand it to mean "many friends from the set of my friends".
There is little agreement among grammarians on the labels used for word classes/parts of speech. This is something I think we need to accept.
I wouldn't go that far. The POS of a very small number of words may be in dispute, but in general there is agreement. Logic and evidence usually prevail, as it does with "many" (see above).