We had a brief few years in the sun when at least the left-wing did genuinely care about gay and lesbian rights, and they're still milking that today, but they no longer care about gays or lesbians (especially not lesbians). That's not new and exciting, that's just a return to the status quo. For most of history left-wing parties have opposed gay and lesbian rights just as much as right-wing parties (for example, left-wing parties in Australia opposed marriage equality pretty much right up until the govt was legally forced to implement it)(and it was a right-wing party actually in govt when marriage equality was implemented).

These homophobic left-wing parties had their excuses at the time, just like they have their BTQ+ excuse today. For most of history you could very much be left-wing and homophobic. You could say things like 'oh it's fine to fire someone for being gay/lesbian, free speech, whatever' and have other leftys clapping like seals, just as they do today about TERF lesbians and genital preferences.

The only real difference today is that it's not cool (and borderline illegal) to just say you hate lesbians. Both the left and the right will frame their lesphobia as 'ackchually we really super duper care about lesbians' because they know people will just believe that, rather than think about the plight of a marginalised minority they've always hated. The left-wing version of this is 'we support the LGBTQ+' and the right-wing version is 'we support adult human females', meanwhile BOTH sides (and every other possible side) routinely indulge in lesphobia, will only bring up lesbians when it serves them, and consistently do more to harm lesbians than help us. But it's fine because they said they support lesbians.