With a bit of googling I found that this form means "Although; But; subject may well do N, but not S; ~することはあっても~することはない", and I found this answer, which as far as I understand confirms that meaning (「~こそすれ」は「~はするけれど」の「~」の部分(動作)を強調しつつ堅めに言い換えた表現です).
I'm having trouble really understanding it, though; for example, in an anime I found this sentence:
ゲーム部の人たちを尊敬こそすれど滑稽だなんて思いません
which would translate as "I respect the members of the game club, but I would never think of them as ridiculous"; I get the general meaning, but that "but" (はするけれど, ~することはあっても~することはない) sounds really odd to me: "but" seems to create a contrast, like "I respect the members of the game club, but I would never join it" or "I don't respect the members of the game club, but I would never think of them as ridiculous", so in that sentence I'd rather read something like "I respect the members of the game club, (and) I would never think of them as ridiculous".
How should I read this structure?