I have a feeling you already know there's a conservative movement to roll back access to contraception (Burwell v. Hobby Lobby?), but if you needed any further proof, mainstream far-right conservative Clarence Thomas explicitly wrote in the Dobbs opinion:

"In future cases, we should reconsider all of this Court's substantive due process precedents, including Griswold, Lawrence, and Obergefell,” Thomas wrote in concurrence. “Because any substantive due process decision is 'demonstrably erroneous,' we have a duty to 'correct the error' established in those precedents"'

and many sibling posts have cover the current legislative initiatives to restrict birth control.

So yes, the far-right does want to roll back access to birth control, the right to marriage equality, the right to privacy between consenting adults. The American far-right wants a big brother government enforcing their personal morality on the whole country, right into our bedrooms and bathrooms.