Some people think they are especially religious but don’t control their tongue. Here’s how James puts it in James 1:26:

If anyone considers himself religious and
yet does not keep a tight rein on his tongue, he deceives himself and
his religion is worthless.

I’ve worked on this question, not only because as a teacher and writer I sometimes have to render judgment and because it is a temptation to be harsh, but because the very person who wrote these words — and the Person’s teachings he makes his own in this letter — said some very harsh things.  Notice these things:

James 4:2: “You adulterous people, don’t you know that friendship with the world is hatred toward God?”

James 5:1, 5-6: “Now listen, you rich people, weep and wail because of the misery that is coming upon you…. you have lived on earth in luxury and self-indulgence. You have fattened yourselves in the day of slaughter. You have condemned and murdered innocent men, who were not opposing you.”

Clearly, and again like Jesus who spoke of not being judgmental but could utter strong words (Matt 7:1 and Matt 23), James does not mean by bridling the tongue a total silence when it comes to discernment.

Here’s my stab at it: James is against (especially) the teachers uttering words that ruin the community (cf. James 3:1–4:12). To bridle the tongue is to learn the tongue for what is right, to say the right thing at the right time, and to say the right thing in the right way. Some will take this view as an excuse for being harsh, but others will see it for what it is: a powerful warning to teachers to pay special attention to what they say and with whom they say it and how they say what they say. God be gracious to us all.