Just to throw in my two cents.
Although I do believe there is something inherently wrong with a same gender union (be it in or out of marriage), there is a Torah point I would like to raise.
The OP wanted to know if there is an issue with Same gender relationships outside of Halacha. A valid Question.
Reb Yochanan (I think) says (brought in Rashi somewhere in Devarim!) A person should never say, “Pig is disgusting”, rather it is probably delicious, however the Torah forbids it.
I think that the reason for this is simple.
If we don’t do something because ‘we feel’ then we can change in a second.
Ask the average American if he believes that murder is Ok.
He will hopefully say “of course not”
Then ask him why is many countries, murder is considered good.
If you wanted to be a good German in the ’40s, you had to believe in killing Jews.
If you want to be a good Muslim (according to some) you have to want to kill Jews/westerners etc.
Therefore, ‘I feel’ that murder is wrong, could easily change.
If not by you, then maybe your children or grandchildren.
So if we say that “gay unions” are disgusting/immoral etc etc, that is a short lived feeling.
Saying the Torah forbids it, means, it will NEVER be permitted because the Torah will never change.
I hope I have explained myself clearly!
Thanks for reading!