The right has had majority control of the federal government for most of the last 25 years:
Divided government in the United States - Wikipedia
As the far-and-away leader in cable news ratings, Fox News is very much "mainstream" and they are very much on the right.
Conservatives dominate talk radio:
List of most-listened-to radio programs - Wikipedia
The most popular podcast in America right now is The Joe Rogan Experience; and the most popular English-language Youtube channel is PewDiePie. Neither host is a leftist.
WWE is the #4 English youtube channel and does not cater to a leftist audience.
I'm not sure how you'd measure influence on Twitter and Facebook since they're dominated by non-political entertainment, sports, and products. Either way, the right has much more power and cultural influence than you seem to think.
Perhaps that's because Marx was an economist whose ideas didn't require the atrocities with which they were later associated whereas those atrocities were a core part of Nazi philosophy.
That's a lot of poppycock. Conservatives aren't some tiny, sequestered minority whose ideas never see the light of day. I used to be a conservative and I left the movement because I found the bulk of their beliefs to be rooted in faith-based dogma rather than evidence. Conservatives are partly to blame for their own lack of stake in academia and journalism. They've chosen to retreat from the more established institutions in those fields; they've lampooned those organizations to their children (thus disincentivizing them from pursuing careers in those fields) and when they've tried to go and recreate these institutions with a more conservative leaning, they've done a rather lousy job of it.
For example, conservative media certainly has enough money, but where is the conservative equivalent of the NY Times or the Washington Post doing in-depth long form journalism? Where is the equivalent of NPR doing solid reporting and thoughtful human interest shows? Where is the conservative movement in the film industry where stories of traditional conservatives ideals of family, loyalty, and sacrifice do quite well? Instead we have Fox News, Rush Limbaugh, The Daily Caller, and a bunch of other angry (mostly white men) shouting at people, trying to make them angry. When they try to put out something more narrative heavy, it winds up being cloying and ham-fisted like all the treacle on the Hallmark Channel.
If conservatives want a presence in these institutions they have to actually do the work necessary to be qualified for it instead of churning out the mindless schlock they usually pawn off on their audiences.
Fox news is one right-wing channel in a sea of left-wing ones. Left-leaning output far exceeds right-wing output on social influencers like Facebook and YouTube because the companies that run those platforms, like Google, are left-leaning and they actively demote and censor conservative content and even design their algorithms to filter out content that goes against the "sanctioned" narrative or favored point of view.
Buzzfeed and other SJW and left-leaning channels have far more viewership than any conservative ones that I know of. And you can compare searches on Google vs. DuckDuckGo to see Google's bias, which was exposed during the last election. (You can find videos about that on YouTube if you're interested, if they haven't been removed.)
What a leftist considers "neutral" is probably more left-leaning than they recognize. Leftism is the status quo, and everyone has to live in its influence to some degree, unless they stop using the computer and live out on a homestead in the wilderness somewhere.
It doesn't matter what Marx's intentions were, just like it doesn't matter what the intentions of politicians and political activists that support and advocate his ideas are. They're ruinous ideas that are contrary to actual human nature and always result in failure and human suffering. People aren't cattle and they're not basically good by nature. Any ideology premised on those ideas/assumptions will produce disastrous results because it denies reality.
"The road to hell..." as they say. The millions of people killed by Marxism's good intentions are just as dead as those killed by Hitler's regime, and far more in number.
Hitler, incidentally, had good intentions too; and if you don't believe in objective morality, who are you to say he wasn't noble? He had the best good of the German people at heart.
What looks and sounds evil and does harm is more easily identified and rejected than what looks and sounds good but does harm.
I don't advocate conservatives taking over society the way leftists have because I believe in individual freedom (something leftists claim to believe in but only if it's freedom to do and think what they agree with and approve of; otherwise they want it banned).
Many conservatives, libertarians and classical liberals feel the same way, and that could account for why they're less militant about spreading and taking over institutions and the media as the left is. We don't want to conquer and control, we just want the freedom to live as we choose according to our own conscience, and we believe in giving others the same, with only as much government regulation as is necessary to maintain peace, order and safety; whereas the left believe in controlling other people for what they believe to be the greater good, like Marx did.
Obviously not all conservatives think that way. Some do want to conquer and control, mainly those in the political sphere. But I think you'll find that most fall into the "live and let live" category and therefore resent having leftism crammed down their throats just as much as leftists resent having Christianity crammed down their throats.
I personally don't believe that Christians should attend secular universities or public schools or try to Christianize them. I do think that their personal freedom of religion should be protected there if they choose to attend them, as should that of those of other beliefs, equally.
I believe that private institutions and businesses have the right to operate according to their own principles and should not be compelled by the government to change them. If people don't like the policies of a private institution or business, they have the freedom not to attend or patronize it. But leftists want to put them out of business and force them to violate their principles.
Leftists see authoritarianism as a necessity for the greater good. But what is good is highly subjective and should be for the individual to decide as much as possible, and the government as little.