Can a trumpet be tuned

It depends on what you mean. If you mean, is the Trumpet a transposing instrument, yes, if you're talking about anything other than a C trumpet, which is in concert pitch. Trumpets in all other keys are not concert pitch. For instance, when playing on a B-flat trumpet, the note that you learn as a D is actually a concert pitch of C.

If you are asking do trumpet players have to transpose music, the answer is, yes, generally speaking, but it depends what music you are playing. For instance, if you are playing on a B-flat trumpet and playing music written for the B-flat trumpet, you play the music as is. If you are playing on a B-flat trumpet but playing music written for C trumpet, you have to play the music up a step.