Simply put, the problem with conservatism is and always has been that it is a reactionary ideology. One that is against change by default and seeks to regress, to a "traditional" and "good ol' days" world that never truly existed. Reactionary movements are almost universally not looked positively throughout history. Conservatism has also always historically benefited the wealthy/ruling class over the poor and marginalized. Conservatism and fascism, though obviously not the same ideology, are closely linked. There are four typical factors in my mind which cause an individual to support conservatism: lack of education/exposure, bigotry, lack of compassion, and greed. In the future, conservatism will always exist as long as the four aforementioned causes also exist.
Conservatism in the United States seems to be winning the "culture war" right now, less because of its own merits, but more because it is the alternative to an insanely strawmanned view of the "left" alternative; an intrusive, big-government, globalist, hyper-politically correct world where there are millions of genders and sexualities, white christian men are under constant attack from academia, media, and Hollywood, freedom of speech is banned in the name of protecting oppressed groups, masculinity is sexist by default and men are becoming feminized into submissive, weak "soy-boys", students are taught far-left anti-American propaganda in schools and universities, Antifa/BLM vigilantes roam the streets attacking random bystanders and "burning down cities", there are completely open borders, innocent men are jailed over the mere allegation of sexual harassment, people are "cancelled" for speaking universal truths such as "we are all equal" or "not all cops are bad", etc. I could go on. Conservatism is instead presented as a pro-freedom, equality of opportunity, "live-and-let-live" alternative, when in actuality, that is libertarianism, not conservatism. I'd even go as far as saying that the Democratic party's failings, focusing too much on sounding "woke" on social issues while not doing nearly enough to substantively address the massive and growing income inequality, expand healthcare and university access, workers'/union rights, solve issues caused by institutionalized racism, end the wars, solve climate change, etc, is what empowers conservatism.
And of course, the fast-growing social media platforms and influencers that are funded by billionaires and other dark money such as PragerU, TPUSA/Charlie Kirk, Louder with Crowder, Ben Shapiro/Daily Wire, DC Draino, etc, are the biggest contributors to the conservatism winning the "culture war" by promoting their strawman/ad-hom attacks and misinformation. This is being done not because the founders and donors of these organizations are deeply passionate about Americans having "traditional values" and whatnot, but because it is a calculated strategy to keep the masses perpetually distracted from class issues, fearing "the left" instead of the greedy politicians and corporate lobbyists as well as the power structures that keep screwing them over. The left, sadly, isn't as effective at promoting their progressive ideologies to the masses and moving away from the stereotype that they are all hyper-woke crybaby SJWs. Part of that is to do with there being more ideological factions on the left (excluding the alt-right, conservatives seem to be unified on nearly every issue) as well as the lack of funding. As aforementioned, the wealthy and powerful have always promoted conservatism for a reason.