Yes it can!
For example, a Christian may consider bestiality immoral since the bible forbids it (Leviticus 18:23). A secularist on the other hand may consider bestiality immoral since there is no way an animal can consent to intercourse and thus any act of bestiality is considered rape.
The Christian's reasoning is not logical whereas the secularist's is logical.
I also disagree with your statement that logic is not absolute.
Are you claiming that the christian opinion is not logical because the bible is possibly not true, or is not absolute in meaning? If so, isnt someones belief in the bible/god opinion? So how can it be not logical if they believe the bible is true? By their logic, it makes perfect sense.
It thats not the case, sorry, i might be missing what you are getting at here.