Actually it does have to do with "LGBTQ " issues because:

1. The transgender agenda aka the TQIA+ has completely co-opted the LGBT label at this point, to the extent that actual lesbians and gays are being cancelled from our own spaces due to same-sex attraction being classed as "transphobic"

2. The transgender agenda justifies itself in entirely post-structuralist and postmodernist terms according to Critical Theory, saying that gender is socially constructed and not biological or natural

3. This is the same Critical Theory in the form of critical race theory that simultaneously says that race is not a natural, biologically grounded feature of humans but is completely socially constructed, and also that it is in the nature of white people to oppress all the other races

4. which is the justification of the founders of the BLM movement

5. which invented the term "woke" to describe itself

Therefore transgenderism is entirely woke, as is the "LGBTQ" community which at the moment only represents trans people, not homosexuals as it claims.

I agree with you that woke has nothing to do with gender equality, except in as much as woke transgenderists are undermining and subverting gender equality by pushing for men to be allowed to categorize themselves as women, thus bypassing the legal protections that women need to protect ourselves against male oppression and violence, given that males are physically stronger than us.