that if there is no good reason to consider homosexuality immoral, then ..........
Surely this is the crux of the matter
Both the relatavist and the absolutist DO have "good reasons" on which they make their moral judgements.
The absolutist has their external source of morality (e.g. the bible)
They consider this a good reason
The relatavist has their rationally thought out overarching framework (e.g. the freedom of individuals to pursue happiness as long as they do not hurt, harm or interfere with the others pursuing the same freedoms)
They consider this a "good" basis for reasoning their detailed moral judgements.
Neither the relatavist or the absolutist are making moral judgements on the basis of
no good reason
That would indeed be unjustified and open to the sort of attacks you are making.
However your complaint against relatavism on the basis of
no good reason
is a straw man argument.
Bringing nature into the argument is also a dangerous game. If homsexuality can be shown to natural does that make it right in your eyes? If paedophilia can be shown to be natural does that make that morally right? Is eating hotdogs natural? Does that make it morally wrong?
Why should what is natural have any bearing on what is morally desireable or vice versa?
Edited by Straggler, : No reason given.