Do they have any influence on mainstream Catholics? Yes, somewhat.
Does the average lay Catholic hear about or care about this stuff? No, the average Catholic doesn’t even attend Mass on Sundays. But this stuff does trickle down to faithful Catholics in the pews who are paying attention. A couple months back, liberal papal apologist Mark Shea lamented that a seminarian at left-learning (!) seminary told him that 40% of his classmates were fans of Taylor Marshall, Cardinal Burke, Father Z, Steve Skojec et al. and estimate that at conservative/traditionalist seminaries it’s more like 70-80%.
Interesting, thanks. No wonder the pope told priests to get rid of the “rigid” seminarians.