The problem is their definition of “do your own research.” This problem is probably largely unavoidable because, human nature. But it’s made markedly worse by what has clearly been a long term, mass scale failure of the education system to teach most people to think clearly.

It's become a thing because saying, "do your own research" is infinitely easier than investigating the current accepted body of knowledge to risk wasting months or years of your life only to find out that the current accepted body of knowledge was already correct.

"Do your own research" is the "trust no one" of the 2020's. Anyone who says it simply wants you to go away and isn't interested in debate and is unwilling to accept any information that might imply that they are wrong. If someone says "do your own research" to you and you are not both currently scientists working in the same field then it is safe to ignore them and everything they have ever said (and quite possibly everything they ever will say).

If this is the only rhetoric, it fails all the other criteria I laid out. If it's not a useful, predictive, and positive worldview then this is not a good group to be in.

As for trust or distrust in authorities. There are many authorities that give you a good reason to trust them, namely a track record of telling the truth and acting in your best interest. There are also many authorities that give you a good reason to distrust them, by abusing their authority for personal profit, exposing themselves as an enemy, or selling out their built up goodwill to the highest bidder.

I don't think this is ideologically problematic. It's just that the people rejecting the authority have very little practice doing research.

Not just that, but if one is researching for confirmation bias then said "research" is pointless.

If there's no willingness to accept that a belief is mistaken then there's no room for reason.

Think for yourself but not like that.