that these same "anti-authoritarian" figures actually support the political and economical status quo and
You are assuming people do things consciously, evaluating all pro/cons. But usually it's not. So if we have a philanthropist, say, George Soros, that gives money to a cause he likes, then the ones against that cause say the people are just puppets. Once you get that label, you are classified, and put into a box (not a literal box, I mean an ideology, and a very narrow scope of it) even if people do not belong in that box and were there just by coincidence.
Back to skepticism/trust. I like your broad definition on that. But I think there is also a classification of "good enough". For example: do I trust the ground to not quake or to sinkhole while I'm standing in a field. Do I trust the tapwater today. Do I trust my electrical wiring in the house to not short-cirquit and cause a fire. Do I trust the other drivers to not make me crash. Do I trust my heart to keep on beating. Do I trust the meteors to not crash into my house. Do I trust the sun to not suddenly stop shining. Do I trust that celestial laws do not change while going collectively into a new region in space (say a highspeed blackhole does a driveby at a few hunderd Astronomical Units and slows down time). Do I trust this rope to not break while climbing at high altitudes. Or parachute to open while jumping. Do I trust this-match-in-my-hand to work and not splinter while I strike it.
In al those cases, I can not say 100%, but it's 90-something.
Sometimes the price on trusting is low (I get another match), sometimes it's high (Don't use fishing nylon to climb a wall).
A real danger, as you pointed out, is when you start building a trust system on top of other things. You get into the "may faulty logic undermine your whole philosophy" realm. And that is scary.
We mitigate it, by having plan B's. But sometimes, there is no plan B.
Example: Before going to the moon, there were 3 theories about how the moon was formed. Supporters of each theory pointed out the flaws on the other theories (if we find this on the moon, then it cant be right), and when they went to the moon.... all three got invalidated. And all three still have echo's in todays science books, even though they are invalidated...