Gender abolition is an ideology that says we should free ourselves of gender. That we should all live as individuals and not "force" ourselves into categories.
This sometimes stands in opposition to the mogai movement that proposes that our individuality can become our own gender. Your unique, or more unique, gender expression can be described with a special name (usually from another language like Latin, German, etc.) and have its own flag and a page on a wiki article.
Both of these ideologies/movements usually (not always #notallradfems) make a distinct separation of sex and gender. Sex is supposedly what you're "born as" and gender is what you "identify as". Gender abolition to many transfems has become a weapon aimed at them to degender and push towards bioessentialism. Sex abolition however is an ideology usually centered around the harm that binary sex has on intersex people, especially to forced medical procedures at birth, through childhood, and the lack of agency they still have in their lives and in medical procedures when they're an adult even. Having a more fluid, encompassing, or eliminated definition of sex can also help trans and intersex individuals face less discrimination with medical procedures, identification documents, and general perception of how we are as humans.
I wasn't able to read the full blog post you linked, but it seems to be talking more for sex abolition than gender abolition. Something that may seem like a small distinction, but generally has very big differences in end goals and who it targets and who it tries to actually help
