You are exactly right.
In the past I have personalized this argument with people. I try to use a named loved one of theirs. A daughter, granddaughter or someone close to them. I use the example of a pedophile wanting to have a sexual relationship them and then I ask the person what gives you the "moral authority" to say they can't have your relative?? Obviously our society has a "code" that finds it unacceptable - but the usual response is "because it's not right." If the person tries to list any reference to a bible they are trapped because bibles of old still have the listed sin of homosexuality which is "normal" to the brainwashed citizens.
When people refuse to have an established moral code they reap this "benefit" of "everyone does what is right in their own eyes." A pedophile, homosexual or bestiality - hey they are "sexual orientations" leave these poor people alone and let them "enjoy" their lives!
You’re using an argument that I’ve developed recently in a more general manner.
Usually the people who try to say that homosexuality is morally OK use relativism as their justification - ie, you can’t impose YOUR value system on others (which is what they are doing with their relativistic value system - but that’s another argument).
They reject the idea of moral absolutes, especially those written down in the Christian Bible.
However, they don’t really think that way. They believe THEIR value system is superior to yours, but the only way that ANY value system could be better or worse than another is by comparing both to an external absolute standard.
So, they either have to admit that their value system cannot be “better”, or they have to accept the existence of an absolute. If the latter, that absolute has to be referenced and agreed upon by everyone. And where are we to find this? aha!