I think your characterization of liberal and conservative is inaccurate. First, there is no central summary of what the views are for these groups.
Liberals are okay with private activities that don't hurt anyone, so they are okay with sexual activities. They think people own their own bodies, so they are okay with taking drugs like pot that don't hurt anyone; harder to say where the line goes with harder drugs. Burning trash in your backyard hurts the environment, and hurts people who live around you, so they are generally not okay with that.
Conservatives want to give you freedom to do what you want, and they say they want to be free to make choices. But of course they want things to be like they were in the past, so they don't like freedom to be gay or whatever. They hate the concept of global warming exists, I think because it leads to their actions might hurt others (like buying a gas guzzler). The problem really becomes apparent when conservatives deny science, in the earth is 8000 years old crowd, or the truly childish fantasy that 99% of scientists are only in it to make money and are happy to lie, that's why there's collusion about global warming.
Conservatives want to have a gun in their house if they want it. The liberals next door might say you are statistically more likely to accidentally shoot someone else or even your own family, so get rid of that to make us all safer - but this is more of a middle ground.
It's not about threatening my world views, I'm a liberal and that's all wrong. Liberals or progressive people want to learn and advance, they want to base their actions off of facts. Conservatives generally make their decisions based on ideology. I have changed my opinions on many things during my life, based on facts and my own experience. When I was a kid I didn't know any gay people, I wasn't sure what to think of them. As an adult, I'm sad to think of how they quietly suffered their whole lives. If cons were really operating based on facts, they'd not be so afraid of trans or gay people, because facts show there is nothing to be afraid of. Facts tell us about the conspiracy in the catholic church to hide predators - there's no international conspiracy to help trans people.