I think maybe some in here are talking about different things while using the same words.
An easy example, just from my own life experience, is the rural/urban and uneducated/educated dividing lines. This dynamic represents me well. The more I've learned (in academic circles and also in life experiences), and the more urban areas I've found myself in (moved from Wayne to Lincoln to Atlanta to Chicago), I've become a lot more liberal in my thinking. This thinking is almost entirely centered around social/cultural philosophies, and almost completely void of policy preferences insofar as they are informed by issues surrounding people.
Why is that? It's because my value system has changed. Value systems naturally change with age, because young people don't really worry about their insurance premiums, the mortgages on their houses, etc., but it's also more than that. Until I left Nebraska, I didn't know any Muslims. The majority of black people I knew were either affluent or athletes or both. Gay, lesbian, and trans people were weird/scary/dirty in my head. All the Latin-Americans I knew were low or middle class factory workers who kept to themselves. As I started to rub shoulders with people surrounding me, I started to realize that my life experience was not a default one ("why are black people so loud all the time?"), but one of many different ones, and one that benefitted from a lot of structures and luxuries that others had never been afforded.
Conservatism as a philosophy is equally valuable and worthwhile as liberalism, because diversity of thought and approach and roles to play is highly needed. Social structures need people to hold onto the integrity and values that might be in danger of being abandoned through progress, just as they need people to pioneer and push the boundaries going ahead, just as they need people to be calm mediators and interpreters, just as they need people to be angry and loud and passionate. Conservatism as the American political system is also valuable for plenty of reasons, but still has a lot of overlap with the uglier sides of our country's history. To conserve is to hold onto, to protect. In politics that plays out a lot of different ways, but one thing it often wants to conserve is a way of life that some would call a white supremacy, that was very prosperous for the founding people group of our country, at the cost of treading on minorities.
Not sure if that makes any sense as I started going off on some random tangent, but generally urban liberalism is found in people being exposed to the plights of others that are different than them, and wanting culture to push on their behalf, imo.
Edit: I want to add that conservatism is pretty natural. Liberalism, when it just becomes a matter of my team winning and the other team losing, is the same way. Because tribalism is natural. It's not bad, it's the entire history of evolution informing the way our highly irrational brains are meant to operate. America isn't natural, and social progressivism isn't natural, and they were founded with highly unnatural ideas but implemented quite imperfectly. Liberalism/progressivism at it's heart, on it's best day, is to take those ideals and to try to flesh them out they have the potential to be.