The policies I advocate are for the real world in the here and now

Just because you advocate a policy for a current issue does not excuse a complete lack of thought into any of its future implications and reasons for existence.

I have never heard anyone say there'd be "no need for sexed spaces" and "no basis" for them anymore.

lol what an argument. I've never heard of tau neutrinos either, but that doesn't make them stop existing.

So in the post-patriarchy utopia as you envision it, there'd be no spaces for lesbians or gay guys that exclude members of the opposite sex?

People have the right to form spaces on the basis of certain shared interests and identities. That is entirely different from legal protections for said spaces because they are necessary to lead a normal life, as is the case with women.

So a world without patriarchy would mean "no basis" for separate male and female sports?

Obviously sports require a sex-based division, as do medical issues. These divisions are based in physical differences in male and female bodies requiring different expertise and different evaluation standards. This is different from spaces that serve to protect women from the social problem of patriarchal violence and harassment. Women are still targeted specifically for their sex, but the reason why they need protection is entirely external.

No separate accommodations for the two sexes in jails and prisons, hospital wards/rooms, LTCFs, dorm rooms, school and scouting trips?

If we were ever to reach a world where men did not pose a threat to women in these environments, yes.

In the post-patriarchy utopia you imagine, women who go to, say, a community swim pool with their teen or adult sons and male in-laws will have to share the same change rooms and showers with them?

If they would get naked with their male parents, why would they not with their female parents?

Will getting rid of patriarchy mean the vast majority of boys and men won't be heterosexual any more, and/or they won't have eyes and dicks?

It's unlikely that most men would be heterosexual if we got rid of the patriarchy. Most "heterosexual" men really just have a fetish for femininity and misogyny. Moreover, you can be heterosexual and not act like a creep, just as homosexual people manage to do.

And that within families and households, there will be no need or basis anymore for the kinds of sex separation that customarily is put in place as children grow up and relationships change?

How exactly do you think gay people are able to function? Is there sexual tension between every non-straight family member?

Such as girls no longer being seen naked by their dads or brothers once they hit puberty? And pubertal boys being given bodily privacy by their mothers - and vice versa - too?

If the same things were to be normal with their same-sex family members, then yes.