No. They can enter into any number of fully enforceable contracts.
They can enter into a contract to lend money. But not if it’s at a usurioius rate of interest. They can enter into a contract to make an investment. But not if it violates the Securities Act of 1933. They can enter into a contract waiving certain rights under law. But not if the waiver is contrary to public policy. They can’t enter into a contract to have sex for money. They can’t enter into a contract to kill someone. Or rather, in each of these cases, the courts will refuse to recognize or enforce such contract. Everyone has the right to enter into a contract to loan money at up to 18% interest. No one has the right to enter into a contract to loan money at 30% intereset (Y. State MV). “How unfair! They are privileging one kind of contract over others!” But my demonstration above shows that the state always does that. There is no recognized right (and no, shouting “equal protection” won’t create one) to enter into any contract you want and have the government enforce it – and that is true even if the government enforces analogous (not identical) agreements as to parties who are situated differently than you (i.e., the 18% lender vs. the 30% lender, or the heterosexual marriage seeker vs. the “gay marriage” seeker). It’s really not difficult to follow, and dissatisfaction with the system that has evolved over half a century of common law doesn’t excuse pretending that common or constitutional law OBVIOUSLY offers you CONCLUSIVE support that it simply doesn’t.
Your problem, or one of them, is that you simply won’t admit that you’re trying to make a policy argument at all, for which you’d have to actually convince people through logic, heuristics, and reasonable appeals to shared principles.
Simpleminded insistence that you OBVIOUSLY HAVE TO BE ALLOWED, as a matter of logic and first principle, to have a contract of “homosexual marriage” enforced is no more legally reasoned or persuausive than arguing that ONLY A MORON WITH NO UNDERSTANDING OF LOGIC AND EQUAL PROTECTION could support a regime in which 18% interest loan contracts are available and enforceable and 19% contracts aren’t – since we live, quite comfortably and constitutionally, in a regime much like the latter example, and no one’s head explodes from lack of “equal protection for whatever contract I want the government to honor and enforce.”
Since you aren’t remotely equipped, as you’ve shown, to argue from first legal principles in a system such as the one we inhabit (are you from N. Korea or somewhere else with no history of democracy or common law? I’m honestly curious – this is sixth grade civics stuff in my country), drop the attempted first-priniciples, jurisprudence and constitutional arguments, and try persuading your fellow citizens (by doing something other than shouting “They’re denying me the right to enter ANY CONTRACT AND THAT’S OBVIOUSLY WRONG BECAUSE OF EQUAL PROTECTION.)”
Just a thought.