Here's the thing: dictionaries are wrong on purpose. I don't mean that as an insult. The job of a dictionary is to tell a person what a word means when someone uses it to them, so if the general public starts using a word incorrectly, dictionaries become obligated to be wrong on purpose. The big C Conservatism you're referring to isn't real. In 50 years, that definition will be erased, guaranteed, because the real definition of conservative dictates political positions relative to the status quo. Conservative as in "favoring free enterprise" is a nonsense definition. People may use the word that way, but it's only connected to the actual meaning of the word in specific times and places, and I don't even know if that's accurate in America right now.
The real political concept of conservatism is the little c concept of conservatism. Disregard what you think a big C Conservative is, that way of defining serves no purpose but to make it more difficult to express your views and to agree with others. I am a Republican conservative, and I am also a progressive, and I'm not going to stop saying that because others have some narrow view of the terms to help them decide who they're supposed to hate.
"tending to preserve or protect, preservative, having the power to keep whole or safe,"… See origin and meaning of conservative.
www.etymonline.com
Read the etymology. Notice the parallels. You are beginning to understand what these words really mean. You just need to forget about that last bit. They don't de facto determine targets. You're just trained into ignorant, and mostly pejorative, uses of the terms. Especially given where you live. Let them have their real definitions. It allows for so much more reasonable discourse and so much more opportunity for agreement.
There is a word for the latter. It's "traditionalists". Unfortunately, there isn't an accepted word for the former, so I do my best. I don't mean unpragmatic progressives, because I'm referring to people who don't care about progress. They only care about change. They only care about opposition to the perceived hegemony. Anti-capitalist, anti-white, anti-Christian movements do not care in the slightest about progress. They have picked the things they feel have power and are determined to oppose them on principle, regardless of whether it help or hurts people. I know these people rationalize their positions, thinking anything with power is hurting people so the only way to help is to oppose them, but that is just self-delusion. You point to any time and place where those in power now were forces for good, and you will be disregarded by some on principle. Those people are not progressive. Many of them will deny any progress has actually ever been made. Those people are purely transgressive. Progressive and conservative are complements to one another, but many of the people who identify as progressive aren't progressive at all, because rather than advocate for specifically changes that might help people, they stand in opposition to all traditions and the status quo as a matter of principle. It is the equal and opposite to stubborn traditionalists, but traditionalists aren't actually conservative, and these transgressives aren't progressive, because neither of those groups give any serious consideration to the causes and effects of the policies they advocate for.