Partisans may object "but in the abortion case it is objectively extending inward and the other perspective is the optical illusion". But that objectivity is a moral illusion.
i personally agree with the recent supreme court ruling that abortion rights shouldn't rest on privacy protections, but rather on a robust reading of the constitution that bodily autonomy is a fundamental right above and beyond states' interests (nation state or US state). i'd extend this to the issues of euthanasia and suicide as well. the state should have a very narrow and rigorously limited set of concerns (foreign relations and interstate disputes, in the case of the US federal govt).
It seems specious to claim this when the states' interests in the body in this regard (as well as gay marriage and any other rights formerly predicated on the right to privacy asserted in Roe) are based on conservative Christian beliefs and mores.
gay marriage shouldn't be predicated on privacy either. two people want equal protection under the law as any other two people who have enjoined their lives together. that's basically it. certainly the gender/sex of those two people isn't the state's concern, because reproduction is not a state concern, but rather a private matter.
But population growth rate (or decline) is absolutely a concern of the state, and reproduction is a significant contributor to that. In fact, one could argue that if a state has an interest in providing health care (including things like contraception) then it must have an interest in reproduction too.
All of those policies can be motivated by a state/federal desire to grow the population. In fact, some people believe that the federal government has a legitimate interest in providing a free (or discounted) service for healthy women to abort healthy children at any stage of their pregnancy, so if the government has an interest in preventing children then surely it can have an interest in producing them.
Notwithstanding the facts that marriage isn't necessary for sexual procreation and that LGBT people can and do procreate, if the primary interest of the state in regards to marriage was to define it in terms of procreation, then the greater concern by far should be heterosexual marriages which don't produce children and rates of divorce. Yet no one is attempting to argue that heterosexual married couples should be required by law to produce a child within, say, two years.
Also, there is a difference between government providing access to services which citizens can choose to avail themselves of, and government legislating reproduction directly. The government doesn't have "an interest in preventing children" in the case of providing access to abortion clinics, rather the interest there is providing access to medical care. The government isn't forcing anyone to have abortions. So the government banning gay marriage in the interest of "producing children," aside from not making any sense as described earlier, isn't a valid countercase to the government providing abortion access.