The "left and gay/alternative community" are not decidedly not homogenous blocks.
Like any other group there are factions and individuals who reject elements of the more widely accepted dogma and believe things not shared by the larger group. I know a few homosexuals who are staunch Republicans, although those are obviously not the norm. Certainly, plenty of the gay community absolutely does reject pedophilia in the same way gun owners reject gang violence. But there are others who are more devoted to the accepted principles of their movement. According to those principles, judging someone for who they are sexually attracted to is inherently wrong, and not celebrating a given sexual orientation or sexual expression - even for pre-pubescents - is tantamount to denying someone's humanity. To apply those principles in a way that does not legitimize pedophiles requires a countervailing principle that I don't think "the left" holds as a group, but rather exists (in pockets) only as a residue of growing up in a culture that by and large does maintain a desire to protect children.
The relentless slide of the Overton Window has continually made positions held by only the most extreme of the "fringe loonies" on the left to very rapidly become not merely generally acceptable but actually required as litmus tests for leftist purity. This is especially clear when Democratic politicians have to defend the fact that they held "progressive" positions just a few years ago which would be considered outright hate speech today.
No one can predict with certainty whether that trend will continue long enough for pedophiles to achieve the same approval and acceptance of things such as encouraging children into transgenderism. Regardless, we're currently at the point (unthinkable just a handful of years ago) where a comedian speaking out against parents chemically preventing puberty in their young children hormone blockers immediately loses their agent and has venues canceling their shows for that specific statement. Avowed Socialists are the new Democrat superstars, despite Socialist being a downright dirty word in elections prior to 2016.
I don't know about you, but I don't think we're done with the descent into crazy, and I don't think it's so ridiculous to see defense of pedophilia or whatever other bizarre behavior on the horizon for the left.
So, are "teh gaze" driving the pro-pedo bus? No, but the portion of homosexuals who support hard left ideology are on it, or at least buying it fuel. And in fairness to those on the other side who are confused, it is, after all, the exact same bus that the "alternative lifestyle community" rode in on to achieve their own goals.