Aside from your remark being snarky and incredibly disrespectful, it's also wrong-headed and incorrect.

Refusal to be a party to abomination is not a retreat from the public square, but a clearing of the decks so that we might wage battle for the truth unencumbered by entanglements in civil law. If the state in effect redefines marriage to be something other than what we understand it to be, by acting as agents of the state we are tacitly acknowledging the validity of that redefinition. By refusing to execute marriage licenses (particularly in states where same-sex pseudogamy is recognized), we make an affirmative statement that (a) we do not recognize the state's definition of marriage; and (b) we reject the authority of the state to impose that definition upon us.

From a pragmatic standpoint, the disentanglement of the Church from civil marriage will protect the right of the Church to refuse the sacrament of marriage to those who do not meet its canonical requirements. You may think it impossible for the state to force the Church to, e.g., marry homosexual couples, or divorced couples or whatever, but a look at the trends in other areas such as requiring religious institutions to hire people who hold views antithetical their beliefs, or for Catholic hospitals to distribute contraceptives, or to provide abortion services, or for Catholic adoption services to bar homosexual couples from adopting, all point to an erosion of conscience exemptions when such run contrary to state social policy.

That said, a Canadian ought to be the last person talking about the Naked Public Square. Canadian politics is almost totally devoid of religious discourse, except when one of Canada's human rights councils is prosecuting someone for a hate crime for expressing what, just a decade ago, was uncontroversial Christian moral teaching.