I'm probably missing an <irony> tag, but consider the evidence.

• Dumbledore told Harry that Quirrell intervened so Daphne could take down Astorga
• As I understand it, all the bullies have been under Snape's tutelage, their entire Hogwarts careers, with the Slytherin bullies having had him as head of house.
• Prof. Sprout was warned off after dealing with Slytherin bullies on Harry's first day

Quirrell's "they have tolerated worse in their hallways" and give a finger from my wand hand, suggest that bullying has been tolerated for a long time.

What are Snape's adult motives and goals? How much of a panopticon is Hogwarts or House Slytherin there? When he tasked 7th-year Rianne Felthorne, presumably with sending the message back via Bullstrode, she lost count of the charms cast and didn't show recognition of them. Harry would have recognized them from Bester and Quirrell. Hogwarts is a centre of power, perhaps funds his Potions research and precautions againts Voldemort's return. Is conditioning Hogwarts students to fear him defending his future position or building a power base.

Are Dumbledore & Snape treating Quirrell as a bird in the hand, under close observation - Bellatrix's escape is still under investigation after all. Who set up the ambush outside the library? Snape or Quirrell? 2PM is too early for Harry's Time-Turner unless the shield was circumvented. Was testing for The cloak of Invisibility a hint from Snape?

I guess he is anti-bullying except when done by people he likes to people he doesn't like?

That's how I'd characterise his attitude in canon. ETA: This includes, in particular, his own bullying of students.