Cheery would 100% march in the parade. She'd get Nobby to go with her, but Nobby would be completely oblivious as to why (he assumed she just wants company).
Moist von lipwig would have pride-themed stamps made; these would inevitably have some kind of issue, which would create some outrage and ultimately make the stamps more valuable as collectors' items.
I don't get the impression that Ankh Morpork ever had anti-sodomy or crossdressing laws, so I don't think the queer community's history with the police would be the same as it is in the real world. Especially because Cheery Littlebottom literally started the Dwarf trans/feminism movement as an officer of the Watch, with the Watch's support.
Dibbler would totally sell pride flags with the wrong colors (and then insist it was the "new, updated version" if anyone questioned him)
The nobility are all scandalized, meanwhile the Seamstresses Guild has a float in the parade
Adora Belle Dearheart is deeply involved with at least one queer organization and is one of the main organizers of the Pride festival, but refuses to answer any questions about why
Ridcully decides the wizards should be involved, and Ponder Stibbons should make a float and organize the refreshments for them to eat while riding on the float. Ridcully's concept of allyship is loudly saying, "Well done, that man!" and pointing at anyone he thinks is exhibiting particularly queer behavior.
Madam Sharn and Pepe release a whole new line of Pride-themed chainmail
Bengo Macarona is embraced as a gay icon
Reg Shoe decides the main pride event is too corporate, and organizes an alternative pride parade for the same time and place; this immediately gets subsumed by the main pride event. Some Omnians show up to Pride to protest and Reg is delighted to have someone to fight with.