Yes!
The longer answer:
"what is logic" is the question asked by logicians and epistemologists. They're still quarelling about it. Read wiki for the lay-man usage.
There would be no "line" between subjective or objective logic. Its a matter of stance.
Realists would say the world happens a certain way, so the thing that describes that way is logic (and correct), things that describe something else are..well, false, stupid, misleading (and not logic).
Wittgenstein said the following about his book "tractatus" which was a highly "logical" book "this is everything we can say about this stuff, this is the way things work. Of the rest we don't need to speak" (go away philosophical critique monkeys!)
Ideologists, relativists and post modernists do not believe in a verifyable external world which is static and unchangable. Rather they take a more relaxed stance towards the external world and focus on the logic of the subject (idealists) or on some kind of meta level illogical stance (relativists and post modernists). For them logic would always be subjective, as is everything else. (See @
mfckr's post as an example).
Wittgenstein wrote a highly "subjective" treatise about language and logic later in life in which he denounces his earlier work and takes a very social constructivist (post modernist) view.
So...in short... Attitude towards logic follows on your empistomological stance which leans on your metaphisical foundations/assumptions (or lack thereoff).
Ofc you can ground metaphysical statements on logic and so forth, we like circular reasoning
Truth is opening an entirely new can of worms, going back to epistemology. If these type of subjects interest you as a hobby, go study philosophy. If you want an answer, go study theology!
TLDR: I left metaphysics for Ethics....for the money!!!! ;-)