Why were gay men executed in ancient times?

More straight men were executed in any period in history.

It was believed to be sinful. 

I only know of them doing that in ancient Israel, and the reason was Because the Old Testament says that any homosexual activity is punishable by death, so ancient Israel carried out God's commands. 

Because it was thought to be perverse and evil. 

"If a man lies with a male as with a woman, both of them have committed an abomination; they shall surely be put to death; their blood is upon them." ... -Leviticus ... Both the bible and koran include passages of "discord" that promote persecution of inferior peoples. Edit these books to raise the level of world tolerance that makes it a better place.

Religion. Pure and simple. 

You are mistaken to beg the question because, in fact, you are conflating 2 separate things. Not "during Ancient and Mediaeval times" because those are 2 separate issues. The Ancients, as the Medieval people referred to them, were Pagan. Pagans before the Roman Emperour Constantine christianised the Empire in 312 and 321 AD, accepted Ovid Metamorphoses and Lucius Apuleius The Golden A** as religious text, believing that the gods were bisexual and men followed the example set by the gods. In 312 AD Constantine donated the Lateran Palace to the Bishop of Rome and, in 321 AD, Constantine made the Bishop of Rome the Pope and made the entire Roman Empire Christian. Immediately in that year, 321 AD on the orders of the Emperour, homosexuals and pagans, particularly Pagan priests and priestesses, began to be murdered. Oh, it was "Legal", the lawful executions of a Tyrant. Just as Hitler made State Murder of the Jews in Nazi Germany "Legal" by signing it into Law making it lawful; nevertheless, it was murder. Read Barbara G Walker The Women's Encyclopedia of Myths and Secrets and you will see a more logical reason to date the beginning of the Mediaeval culture to this single event, than the way standard texts date it. For half a century I have read all sorts of books taking a stab at when the Middle Ages started, alluding to vague periods as though they were lost in the mists of time. Actually though, they were merely lost in the ignorance of the authors. The truth is, that, we actually do have a clear, unbroken, continuous histórical record right from extremely ancient times, right through the Middle Ages, to the present day: in the continuos, unbroken records of the Roman Catholic Church and the authorship of the Jewish Talmud which was compiled over nineteen and a half centuries by the Exilarchs which physically moved from Babylon to Damascus and, when Bagdad was built specifically for the population overflow of Damascus, in Bagdad finishing compiling the Talmood in 1350 AD they'd begun in 598 BC. That scholars and researchers of History have made it an academic standard to ignore both of these huge, complete, and copious bodies of historical record, preferring to comb through fragmentary and broken traces like the Venerable Bede, has made it possible to give the public this vague sense of the "Dark Ages" in which chaos reigned and everyone walked around in mud and wearing the same brown homespun as everyone else in grade B movies when, in fact, there are still stone roads and bridges, aquaducts and paved streets and even running water and working sewage systems dating back to the Pagan Roman empire still in use today, which Mediaeval people walked on, bathed in, lived in. And scholarly Roman Catholics and scholarly Jews have always had access to the written records of History all along. We don't need speculation such as "maybe" the Burning Times didn't "really" get started until the 1100s when disappointed Crusaders returned from the Holy Land looking for scapegoats so started persecuting homosexuals and so called "witches". It's just industry standard to pretend that large periods of History are unknown to us when, in fact, when one stops poring over fragmentary evidence, and simply turns around and looks at the massive complete body of Catholic and Jewish evidence, it turns out that written records have survived quite as nicely as the paved streets of Aachen, the still operating sewage system which the Etruscans built for Rome and, oh yes, the Coliseum which is still standing today in 2020 AD, was still there right on through the entire Middle Ages and never was packed in mothballs. We have clear, crisp start dates for the beginning of the Burning Times, to the written order by Constantine and to the very day and we know the exact numbers and, indeed, the exact names of all of the victims. Speculation is for those who foster ignorance. Before 321 AD you could be homosexual and most emperours openly practised bisexuality, along with millions of Roman soldiers. Precisely on imperial order, persecution began throughout the civilised world in 321 AD. There you have a perfect answer, backed by the historical record.

Homosexuality was considered unnatural and a perversion.

In certain older cultures, homosexuality was more accepted than it is today.

Religion had much more influence back then. At that time, societies based many of their values and laws on religious values.