I don't believe there is any evidence for any of these claims. Rather the opposite: pro-freedom pro-business anti-regulation conservatives have been crying wolf for years now, demanding special meetings with tech companies, demanding special treatment, demanding government intervention, demanding that they be allowed to say anything without consequences.
Modern US conservatives are a minority. How big of a minority depends on how you draw the lines. Republican policy proposals are often (but not always) even more unpopular. Cognitive dissonance (or just good old fashioned politicking) demands some conservatives insist otherwise and see everything as some kind of suppression effort or conspiracy.
It's the whole "conservatism can't ever fail... it can only be failed" thing at work. Or the Simpsons Skinner meme: "Am I Out of Touch? No, it's the voters who are wrong!" If only the big mean tech companies weren't suppressing my clearly superior views everyone would agree with me. No... maybe your views are just way less popular than you think. Maybe instead of being shadow banned people just think you're an asshole.