to tolerate those whom one thinks are stupid
—Don’t expect her to be kind to those who disagree with her viewpoint. She doesn’t suffer fools gladly.

The suffer in this phrase has the same meaning as it has in suffer the little children: “to allow or tolerate.” In Paul’s second letter to the church in Corinth, he writes that he feels foolish having to defend his status as an apostle and teacher. But he knows that “false apostles” are lying about themselves and the Corinthians are eager to listen to their foolish talk:

I say again, let no one think that I am a fool. But if you do, then at least accept me as a fool, so that I too may boast a little. What I am saying with this boastful confidence I do not say the way the Lord would. Instead it is, as it were, foolishness. Since many are boasting according to human standards, I too will boast. For since you are so wise, you put up with fools gladly [suffer fools gladly]. For you put up with it if someone makes slaves of you, if someone exploits you, if someone takes advantage of you, if someone behaves arrogantly toward you, if someone strikes you in the face. (2 Corinthians 11:16-20)

Today, the phrase is most often used in the negative, to say that someone doesn’t suffer fools.