Depends on who you want to focus on. Any conservative can come up with any reason in their head ("it's grotty", "god says no"), but these aren't very good explanations for why its a cultural throughline in conservativism.

I think over time there was a focus on patrilineal property inheritance that slowly spread from the upper class lords down into the middle classes over centuries (say, from the slow death of Rome to late "feudalism" and early industrial revolution). If your kid is queer in some way (particularly first born males), its less likely your property is "secure". The truck and barter of women (or more specifically, wombs) to provide strong healthy heirs would also lend itself to being anti-LGBT. While I could imagine that rationally a gay first born son may "do his duty", it seems pretty unlikely as the aristocracy and the church had a vested interest in keeping things this way (also, the Church sometimes got new clergy from aristocratic queers rejecting the system, which also served as hostages and tighter connections of sorts).

There is this idea of a homogenised past, but I have a suspicion that outside of the aristocracy and clergy that directly associate with them, small villages would have had wildly varying language and culture. The peasantry has less of an incentive to track the inheritance of property, so it seems very likely to me that at least some English villages (say) may have had fairly accepting queer culture. It would be quite hard to study as they didn't write anything down. A part of the liberal-national revolutions is setting out to create the idea of a nation. Someone wrote a book about the French nationalist project, which destroyed a huge amounts of variation in culture in the French countryside. I don't remember what it was called, sorry. I imagine the English/British one was a lot slower (started earlier, aristocracy never quite fell out of favour etc), and still today one can comment of every other village having its own accent (a relic). This wouldn't be to idealise the past either, I imagine some villages took their Christianity very seriously and were very homophobic/traditionalist.

The Church also inherited the idea of Pater Familias from the Romans, the idea that the father of the household owned the other subjects of his house (his wife, his slaves, his children). This is obviously a big part of the patriarchy. You can still see this concept rear its ugly head today in certain forms of daddly masculinity, but it isn't a legal concept now. How much the Church enforced this down to random villages in France would be hard to tell; lots of people were illiterate.

Liberalism and Nationalism, the twin thoughts that permeate our society, inherited many things from the previous feudal system. There was a great migration from the countryside to the cities as farming became more and more efficient. The former middle classes (see: financiers, artisans, merchants) often already in cities became the dominant class (over time) and were faced with a large supply of cheap labour. Not only was this cheap labour useful in outcompeting traditional artisans with division of labour, but it also allowed the middle classes to essentially create a new society centered around massively populated cities (e.g. London, France). The division of labour in farming also helped fuel the reproduction of this society. This new society, based around the locuses of trade, were the new "nations" that were able to leverage vastly more military power both in personnel and material than the traditional aristocracies (look at battle sizes in Europe in the 13th century compared to the 19th century). 2000 Horse-back riding aristo-fucks may have trained since birth to put down peasant rebellions, but a musket shot from a barn will put them down just the same. (NB: Settler colonies evolved a little differently, which is why Canada, Australia, and the US look wildly different to France, the UK, Belgium etc. However, they may have been necessary for the formation of nationalism back in Europe with the vast wealth plundered from Turtle Island, massively enriching trading cities)

The way families and masculinity interacted with Capitalism wasn't a direct one-one path. The Pater Familias turned into the division of labour of the reproduction of society. Just as in a factory one specific guy pulls this lever every five seconds, one specific guy sands down some points etc, so does the woman reproduce society daily (by preparing the household, and specifically the man, for work) and reproduce society generationally (by being an incubator for the next generation). No nationalist ever talks about this particularly openly (at least in my experience), but when they're feeling stressed about their nation's position it comes out about birth rates and the like. However, the echoes of Pater Familias still exist today amongst certain sort of domineering men who think they own their families.

Likewise, the concern over primogeniture and lines of male inheritance have been twisted to serve the same goals. We want more of our nation, we see ourselves in competition with other nations partly defined by wealth but partly defined by sheer numbers and control over territory, and we think queer people stand in the way of reproduction our nation and are insufficiently loyal to the nation.

This also has a lot of explanatory power outside of just anti-queer politics. Anti-feminism and anti-migrant sentiment also come from this. Anti-abortion stuff as well.

(Uh... I hope this made sense, I'm feeling a lot of energy today)