What reasons do the tribunes give to the holidaying crowd for not celebrating Caesar's victory in Julius Caesar?
The tribunes do not want to celebrate Caesar’s victory because he won against Romans, specifically Pompey.
In order to understand what is happening here you have to remember that Caesar’s victor was in a civil war. Not everyone was happy that Caesar was celebrating victory over Romans. Remember that this was an issue of Romans killing Romans. Specifically at issue for Marallus and Flavius is the question of defeat of Pompey the Great.
And do you now strew flowers in his way
That comes in triumph over Pompey's blood? Be gone!
Run to your houses, fall upon your knees,
Pray to the gods to intermit the plague
That needs must light on this ingratitude. (Act 1, Scene 1)
Pompey was a hero in Rome. He was well-loved by the people for his military exploits, and he was a real man’s man. He was also a consul (a high office, sort of like a president).
It should also be noted that Caesar too knew Pompey! They were political allies (and he married Caesar’s daughter). The fact that Caesar would go to war against him would not sit well with every Roman.
Shakespeare includes this scene to tell us that there is unrest in Rome. While the general people may love Caesar, keep in mind that they basically just want a holiday and do not care what it is for. The tribunes, on the other hand, represent the political die-hards who do care who is fighting for what and do not like the unpopular civil war Caesar has just come home from.
To triumph with Roman blood does seem in bad taste. A triumph is a military parade in which you celebrate your victory. Caesar was not willing to acknowledge any impropriety in the war though. It may be worth noting that he is not the one who actually killed Pompey. He was killed by representatives of the Ptolemies in Egypt. It is not likely a distinction the average Roman on the street, or politician in the senate, may have cared about.
Caesar’s days are numbered. Shakespeare is foreshadowing that already with this scene. Yet it also provides some comic relief in the humorous exchange with the commoners, and also sets the stage of Ancient Rome, at least the way Shakespeare is depicting it.