In what ways are Mercutio and Tybalt true to their personalities up to their deaths?
Mercutio has always been between the two houses of Montague and Capulet. He is related to the Prince of the city, and therefore is not allied to either house. He is friends with Romeo, but he is not his kinsman; he is not Tybalt's friend, but has no personal quarrel with him. He fights with Capulets easily, however, and, upon being wounded mortally, emphasizes that he is not of either house by the famous line "A plague o' both your houses" (III.i.90). But after that Mercutio, true to his name (allied to the Roman god Mercury, the god of theives and tricksters) makes grim jokes about his grievous hurt.
No, 'tis not so deep as a well, nor so wide as a church
door; but 'tis enough, 'twill serve. Ask for me to-morrow,
and you shall find me a grave man. I am peppered, I
warrant, for this world. (96-9)
Mercutio has been verbally brilliant throughout the play, thus far, and he is no less in his death. His jokes are meant to hurt Romeo, who he blames, partially, for his death. Mercutio, in some respects, represents authority, because of his relationship to the Prince. Because Romeo is flouting both civic and familial authority (by fighting with the Capulets, and courting the daughter of a rival family,) Mercutio's death is, to a certain extent, a consequence of his actions. Mercutio reminds Romeo of his foolhardiness, even as he dies.
Tybalt, on the other hand, does not lie in between the two houses. He is a member of the Capulet clan, and is fiercely partisan. Tybalt, when taunted by Mercutio, is spoiling for a fight, and, though Romeo speaks soothing words to him, Tybalt will not forgive Romeo for the perceived "injuries" (65) that Romeo has done to him. This fiery and unforgiving nature is similar to his uncle Lord Capulet. He is also very ready to hate someone simply because he consorted with his enemies (the Montagues). Tybalt had no quarrel with specifically with Mercutio, but after he killed him Tybalt does not express sorrow or guilt. He is still angry with Romeo for consorting with Mercutio, and implies that Romeo is to blame for Mercutio's death.
Rom: Alive in triumph, and Mercutio slain?TYB: Thou, wretched boy, that didst consort him here,
Away to heaven respective lenity,
And fire-ey'd fury be my conduct now!(125)
Now, Tybalt, take the ‘villain’ back again
That late thou gavest me; for Mercutio's soul
Is but a little way above our heads,
Staying for thine to keep him company.
Either thou or I, or both, must go with him.(130)
Shalt with him hence.
Tybalt shows that he is a man with the kind of blind loyalty that a clan like the Capulets would require. His only thought is of his honor and his family, not of consequences to others, or remorse over his actions. Romeo almost says outright that he has become his kinsman, but Tybalt takes no time for introspection or reflection. Tybalt, the man of action for the Capulets, dies by the sword.