Firstly, I need to put my mod hat on. You are veering quite close to a "throughout history question." But since you do ask a specific question about the "middle ages" I will embrace my capacity to be flexible.

So this is a deeply complicated question. First and foremost, we need to start with the two major assumptions at the center of your question:

1. ""homosexuality" is a fixed concept that has existed throughout time." Homosexuality (and heterosexuality, for that matter) are social constructs that are less than two centuries old. Certainly homosexual behavior is a simple biological reality, but the idea that one could structure one's identity around sexuality simply did not exist until the last few hundred years.
2. "Same-sex sexual behaviors was viewed with profound and unilateral negativity, causing people to hide their same-sex liaisons from the broader public." Various kinds of same-sex behavior have been culturally organized and structured to be "acceptable" or tolerated at varying points and places in history. Certainly transgressing these very particular structures would have resulted in societal consequences, but there were still spaces for behaviors we might now organize under the gay umbrella (but were not necessarily transgressive within the very particular mores of the time/place.)

Once you remove those assumptions, it is near impossible to answer your question, as the underpinnings of the question effectively do not exist. I hope this did not seem harsh. LGBT history is a particularly difficult field, in part because all the terms and concepts we have at our disposal either did not exist or had a significantly different meaning at earlier parts of history, or in different communities. The word "Queer," for instance, has had roughly four separate and distinct meanings in the last century.
I hope this begins to, if not answer your question, at least recontextualize it.