The first sentence is grammatically correct: let's assume that it has the meaning that you want to convey.
Those who speak English respect those who don't speak English.
As you can see, the phrase speak English occurs in both the first clause and the second. You can therefore make the third sentence using verb phrase ellpisis, because speak English in the second clause is a repeat of one that occurs in an earlier clause.
Those who speak English respect those who don't.
In the second sentence, you are omitting only the object of the verb: you can't do that without changing the meaning, because the speak a language meaning is transitive only, so an object is required. As gotube commented, the second sentence is still grammatically correct, though the meaning is different. This is because the verb speak also has the meaning "say words": this meaning can be intransitive, so no object is required.