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I've recently caught myself spending too much time wondering about several off-sounding compounds I've come across, e.g. browsers list (as in, a list of browsers) and tasks queue (as in, a queue of tasks).

I can't help it, but pluralizing the first word sounds weird to me. I would have said, "browser list" and "task queue".

Which grammatical number is proper grammar?

(This question is quite similar, but isn't answered with regards to this specific detail.)

Although the phrase means the same thing in either case, the singular and the plural mean entirely different things and are therefore both correct and grammatical.

Plural:

"Browsers list" refers to a list of individual elements each of which is a "browser".

OTOH,
Singular:

"Browser list" refers to a list in the class "browser," that is, elements belonging to the class.

Generally though, since we are referring to members of a class and all of them belong to the same class, we use the reference to class, i.e., the singular.

Consider:
User IDs: various elements, all of the type User ID (reference to class).
Users IDs or Users' IDs: IDs of several users. (no reference to class).