What case struck down laws regulating intimate conduct and thud cleared the ground for later challenges of Same sex marriage?

Answer 1

LAWRENCE v. Texas

Having misapprehended the liberty claim presented to it, the Bowers Court stated that proscriptions against sodomy have ancient roots. 478 U. S., at 192. It should be noted, however, that there is no longstanding history in this country of laws directed at homosexual conduct as a distinct matter. Early American sodomy laws were not directed at homosexuals as such but instead sought to prohibit nonprocreative sexual activity more generally, whether between men and women or men and men. Moreover, early sodomy laws seem not to have been enforced against consenting adults acting in private. Instead, sodomy prosecutions often involved predatory acts against those who could not or did not consent: relations between men and minor girls or boys, between adults involving force, between adults implicating disparity in status, or between men and animals. The longstanding criminal prohibition of homosexual sodomy upon which Bowers placed such reliance is as consistent with a general condemnation of nonprocreative sex as it is with an established tradition of prosecuting acts because of their homosexual character.

Answer 2

Lawrence vs. Texas was the case that struck down laws regulating intimate conduct and thus cleared the ground for latter challenges for same sex marriages and civil unions.