What case struck down laws regulating consensual intimate conduct and thus cleared the ground for later challenges for same-ex?

 The correct answer is :  The Lawrence v Texas case

Explanation:   Lawrence defended respect for the right to freedom of all individuals, where the limit of freedom is defined by the rights of others, where freedom does not affect third parties, can be exercised.

Texas was based on the morality of sodomy acts that even if homosexual acts were not involved, the practice of acts of sexual deviation is repugnant to society, because they go against human nature. But ultimately the right to freedom prevailed over others, stating that each person can exercise their sexuality freely since it does not harm third parties.