If we accept Chris's argument, wouldn't that mean that "avant que" would always be followed by the present subjunctive? But that isn't the case. 

There was a similar question before, where Cécile said that both present and past are possible, and I gave a different explanation about the choice.

https://progress.lawlessfrench.com/questions/view/elle-avait-fait-ses-devoirs-avant-qu-il-n-arrive

"Before I started learning French..." that part is asking for the Subjunctive Present tense, which is identical to Present tense for the verb commencer.

You use the Present Subjunctive whenever the time frame of the subjunctive clause is contemporaneous with the rest of the sentence. In this case: "Before I started to learn French" happens at the same time that everybody had warned him about learning its grammar. Therefore it's Present Subjunctive that is called for.

In the excellent answer following your link, Alan, you say:

"In general the past subjunctive is only used when the action in the subordinate (i.e. subjunctive) clause precedes the main clause. It's the relationship to the main clause that is important, not whether it's in the past now."

That's exactly what I said, too. With avant que the same idea applies, even though it is in maybe a slightly looser sense. You use the subjunctive present when the two actions overlap: you stress the temporal continuity. The past subjunctive emphasizes that the first action definitely ended before the second one started.

I find this a very natural extension of the general principle.

I did say that, but then I went on to disagree with myself. I don't see it as an extension of the same principle in this case, but rather a question of aspect (completed or not), since the subordinate clause can never precede the main clause. 

The two actions can only overlap when you use the past subjunctive. It's the present subjunctive that "emphasizes that the first action definitely ended before the second one started".