It seems to me there are two types of conservatism: concern about a change to society that does not have a clear evidential basis (which I'll call "small-c conservatism"), and a desire for other people to not have nice things (which I'll call "capital-C Conservatism").
If you read early radfems' complaints about trans women, you'll see concerns about men infiltrating the burgeoning movement to subvert or destroy its ability to effect much-needed substantial societal improvements for women. Nowadays, internet access and 10 minutes can disabuse you of this notion – but in the past, you'd have to have talked to an out, activist trans woman (who would often adhere to a different school of feminism to you, which if anything is evidence that she is dangerous to the Cause!) or had the right zines circulated to your doorstep (not really an option until the 90s, by which time it was generally understood that Transphobia Bad, the debate was about to what extent trans women's experiences were central to the Cause ("only tangentially" versus "in every respect"), and everyone knew you could pick up a Judith Butler book from your local library), to receive evidence to the contrary.
Likewise, the Catholic Church's conservative opposition to eugenics: they raised concerns about the human rights of those subject to eugenics practices, and later added secular arguments as justification. Contrast their opposition to trans people, which is… theologically confusing, to say the least: the existence of trans people "erases differences" (Galatians 3:28), distorts the image of God (Genesis 2:22), and (I seem to remember one bishop claiming) has already killed God… somehow. (Perhaps Pontius Pilate was secretly transgender? (This is me being silly.)) The justifications are all over the place, as is characteristic of post-hoc rationalisations of Conservative bigotry: replace the vague unevidenced claims about God with vague unevidenced claims about "nature", and the Catholic claims become the same rubbish as TERF claims. (Obligatory note: many Catholics do hold coherent views on this topic: I'm talking about the overarching organisation, not the people, or even all parts of the organisation.)
Small-c conservatism is a strategy, and isn't right by accident: it's an application of the same principle as Chesterton's Fence. Capital-C Conservatism is about denying resources and happiness to perceived enemies, while harming them as much as you can rationalise while still calling yourself a good person. (There are no capital-C Conservative policies that do not involve hurting people, prohibiting social mobility, or restricting what kinds of people are allowed to exist: many of them can't possibly qualify as small-c conservative policies, because they're only "conserving" an imagined past. Anti-immigrant sentiment in North America is one example: https://xkcd.com/84/.)
To undrape the cloak, we can look at how people talk about their ideas, and how they respond to criticism. (And remember not to focus on those calling themselves "conservative". Many "progressives" are actually capital-C Conservative, with a different – but no less harmful – idealised-state-of-nature: many modern-day eugenicists work in autism "charities", promoting "progressive" torture "therapies".) Unfortunately, this does not tell us which ideas are good, and which are bad: to find that out, you have to look at reality, not study rhetoric.
Most people may want good things for most people, but many people wilfully delude themselves about what "good things" means. Those, perhaps more so than the liars, are the dangerous ones.