Pride Parades were not about "demanding acceptance." They were celebrations of pride, a completely different concept.
The first Pride parades were held in neighborhoods that were mainly gay (in San Francisco, it started on Polk St., but then the Castro became "Gay Central" by 1976), so that the gay community could participate in our own celebration. (House party, anyone?!?)  We were not asking for the straight world's acceptance. That actually happened later, when we boycotted companies that openly called homosexuals deviants of some sort - such as Coors beer once did (among others). Once we boycotted - and saw the power of the "gay dollar"  -  they "saw the light," (and saw their sales drop) and suddenly became "enlightened. THEY came courting US. WE did NOT court THEM. And since these corporate giants courted us, they had no choice but to to affirm their "support" of gays, and develop corporate policies of non-discrimination. It was all very interesting to watch.
The San Francisco Gay Pride Parade - for many, many years, originated in the Castro, went down Market Street and then to Civic Center (near City Hall). It was only AFTER corporate sponsors wanted to participate ( the late 80s or early 90s - I forget which) that it moved down to the Ferry Building in San Francisco - at the waterfront, and then the parade route extended twice as far (to the Civic Center) - and became 5x as   big, until it became San Francisco's largest parade. (That took a while, maybe 7-10 years.)
But it was never about demanding acceptance. When you're already proud of who you are, you don't NEED to demand acceptance. You just ARE.
Now, Stonewall was about demanding acceptance, for sure! But not the Pride Parades. That's why the first word after Gay is "Pride."  In San Francisco, nobody needed to demand anything: we are a quite powerful force in city politics and have been since 1975. By the time AIDS kicked in, other than individual stories of discrimination, we were a highly mobilized force to be reckoned with.
Besides, we were too "pretty" to have to need to "demand" acceptance in SF. And as society overall values "beauty," we had  already had that packaged in  24-karat Gold (not gold plated).