<< There are many verses in the Bible that may imply unpopularity should be taken as a measure of correctness of theology, so it's easy to see where some get that idea, >>
Your further explanation is good -- but there is more at work here. This is very common logical fallacy, beyond the argumentum ad populum I mentioned before.
Let me lay it out logically:
Premise: If our ideas are from God -- God-haters will dispute our ideas and oppose us.
Premise: There are people who dispute our ideas and oppose us.
Conclusions: Those people who oppose us are God-haters, and our ideas are from God.
The conclusions actually reverse the if-then statement:
In logic:
P-->Q (If P is true, then Q is necessarily true).
Q (Q is true).
Therefore, P (P is true).
This is known as "affirming the consequent," and it is a fatal error in logic. P is a sufficient condition for Q, but Q is not a sufficient condition for P.
See it? In this case -- they are saying:
* P->Q = If our ideas are of God ---- then we will be opposed.
* Q = We are opposed.
* Therefore P = our ideas are from God.
This leaves out the possibility that we could be opposed for a lot of other reasons, including the fact that our ideas are NOT from God. Even if it were true that the rightness of one's ideas will cause opposition -- that does not mean that any opposition to one's ideas means that the ideas are right. That is "affirming the consequent."
I hope I have explained this well enough. Apart from the self-delusion involved, it's just flat-out illogical.
Now I await the inevitable response in someone's mind: But God's thinking is far above your man-made reasoning.