It's a long-established principle that parents can "opt-out" of having their children take part in certain sex education classes they may find objectionable for a variety of reasons. Recently, some have even proposed "opt-in" requirements. One proposal in Utah reportedly "would require all public schools in the state to obtain written consent before providing human sexuality instruction to students, holding harmless those students who don't enroll." Such a presumption maximizes freedom; it expands the distance between the heavy hand of the state and individual rights. It doesn't entirely disconnect the two, but certainly keeps a healthy distance between them. And these parental "opt-out" requirements have widespread support; many understand why they exist: we want to protect individual rights and the freedom of families to raise their children and govern their family unit as they see fit.
Such "opt-out" requirements have an analogue in conscience exemptions in the abortion context. For years, although abortion has been legally protected as a right under the Constitution (erroneously, I might add), our law has also protected the consciences of those who disagree and ensured they are not forced to take part in practices which violate their beliefs. This also maximizes freedom for all Americans.
Similarly, such exemptions naturally follow in the context of same sex marriage, should it be declared to be protected as a constitutional right. In that case, it would be the default position that individuals desiring such marriages would be able to legally enter them, and thus legislation protecting those who disagree from being forced to violate their beliefs through compelled participation in the process of such marriages would be absolutely necessary. Such legislation has already been proposed. At the federal level, the First Amendment Defense Act would provide such conscience exemptions. Similar protections are needed at the state level.
Like parents who want to (and are able to) "opt-out" of having their children exposed to certain matters at school, many have wanted to (and have been able to) similarly "opt-out" of forced complicity in abortion. It is quite logical that many will likewise want to (and should be able to) "opt-out" of forced participation in the process of same-sex "marriage." In all these cases, the "opt-out" protects individual rights and maximizes personal liberty. It is the quite natural, logical, and freedom-loving position.