I wonder what Jonathan Edelstein's speculations on this might be; those should have some weight and be of real interest.
Subjectively, when I learned of the ruling as a young adult at the time, I was not merely saddened by the setback of general human rights--the
grounds that the reactionary side argued were quite scary in themselves. IIRC, the Court ruled that the law does not have to be rational; that a policy invading the privacy of freely consenting adults that has no compelling logical argument for it can be based on mere precedent--because our ancestors bashed gays, we can (and indeed, should) carry on with that, for the sake of mere tradition. A mindset more squarely against the spirit of the American Revolution is hard to imagine.
By 1987 I was already deeply skeptical of the good will and still more the sound reasoning of the US conservative faction, but I would hope that the sheer unrelenting meanness of this mindset was brought home to people more "on the fence" as I was just a few years before, and that its stunning illogic and casual brutality was apparent not only to the converted such as myself but people who had more faith than I ever had in the soundness of the conservative position.
Therefore, while upholding the right of state and federal governments to target gay people for persecution was an ugly and painful outcome, I feel
Bowers v Hardwick OTL was a double-edged sword; a short run victory for reaction but corrosive for their own position, undermining support and reducing it to a hard core of committed bigots, cutting them off from claims to be in line with the American way.
Had the ruling gone the other way, as it probably would have if Justice Powell had given it more than a half hour's thought, then it probably would be progressives who became more complacent whereas reactionaries might have been more energized and less discredited.
But I don't mean to suggest this one case was all that crucial--save of course in the matter of actual law and treatment of gay people. The mean-spirited illogic of reactionaries of the era was evident across the board; the fact that progressives had a hard, uphill struggle--and yet, when it came to a showdown in terms of real popularity at the polls, progressives stood a good chance because they had logic and the American way on their side--these playing conditions were endemic to the 1970s, 80s and have merely become more stark realities since.
In the bigger context then, I wish Powell had given the case the consideration it deserved, had reflected on what kind of society can give police a warrant to break into one's bedroom and ascertain which sexual practices one likes to use and toss one into prison if they see the wrong moves.
Dissenting Justice Thurgood Marshall called the case a "no-brainer," mentioning that dismissal of the charges and striking down the laws followed from the 1969
Stanley decision, also involving the state of Georgia--in that case, police with probable cause to search for gambling paraphernalia found none of that but instead some films which they viewed and found were pornographic--the Supreme Court eventually ruled that information kept private and not brought into public view was protected.
Powell, I gather from some reading I did long ago on the subject of
Roe v. Wade (where he was also the swing vote) was a rather conventional man; in the abortion case he thought long and hard, and consulted with women on his staff for their perspective, and realized conventional views did not properly consider points of view generally kept suppressed. He might have done so here too; although he believed he didn't know any gay people he had one on his staff--but the fact he didn't know that speaks to the real issues at hand.
Namely, in my opinion, that the basic reason for anti-gay feelings and practices is that society finds it useful to have sticks lying around handy to beat any dissident with; accusations of homosexuality do not have to be true to be effective. Scapegoating serves a social function. But not one that a liberal society can openly acknowledge without undermining its own legitimacy! That his own gay staff member was closeted and discreet about it undermined his own interest in this case and gave Justice Powell a distorted view that the conservative faction in the case and generally sought to maintain.
Ironically, the law that the Court majority upheld here were not focused, in their wording anyway, on homosexual behavior--they applied to any persons performing the specified acts, even to a legally married, opposite sex, husband and wife couple in the privacy of their own bedroom. The fact that they were only selectively enforced against same-sex couples should have been a red flag of discrimination, and also the Justices should have noticed that all their arguments for continuing such discrimination had no application to the law at hand, which did not refer to the genders of the people involved. Instead of course the selective enforcement led men like Powell to consider them as applying to other people and to fail to put himself in their place, as he did empathize with women in
Roe.
Well, as I say, my impression of the case's public impact was that it tended to rip the mask off. People determined to oppose gay rights doubtless got comfort, people committed to them would of course be outraged by any decision that upheld Georgia, but for the people in the middle somewhere, it was pretty raw that the Court would say we can and should discriminate "just because, so there!"
Had it been decided rationally, I think matters would have been much as OTL anyway, except for specific protections gay people would enjoy and deserved to. But the culture wars have many fronts.
I suppose with such a precedent in hand, the question of the rights of gay people to serve in the military (and police forces etc) would have been pressed harder and earlier--but compliance might have been long delayed anyway. After all if the
Stanley precedent, of freedom in privacy, had governed Powell as well as Marshall, the military resistance could argue compellingly that military service is not private; public values prevail.
So the long process of the mindset of the public evolving over decades and generations would probably be necessary anyway.