This clause does not, and has never required, any state to accept as legal that which it specifically prohibits by law, disingenuous contentions notwithstanding. To interpret it otherwise is to effectively grant any state the ability to override the laws of any other state, which is absurd. You don't get it but thats OK, neither did the British Colonel who built the Bridge Over the River Kwai until the very end. Here's how it works:
1) Massachusetts SJC by a plurality of one justice dictates that homosexual "marriage" will be the law of that state.
2) The FF&C clause of the US Constitution requires the federal government to honor that marriage and issue treat homosexuals as married for purposes of the IRS, social security, Medicaid, Medicare et al.
3) Homosexual couples in other states sue the federal government under the equal protection clause of the US Constitution for the same "rights" that homosexuals in Massachusetts are entitled to. SCOTUS rules in their favor.
4) Voila, homosexual "marriage" is a fait accompli and nary a legislature has ever voted on or approved it.
The scenario you describe appears to use the wording of the 14th Amendment, which has also been used for countless other federal abuses, as a means to actually circumvent the sovereignty of the states.
Why not instead change the 14th Amendment, and put that and countless other related problems to rest? I am not saying the Constitution is perfect as amended, just the opposite: much of the trouble we have today are the results of poorly considered amendments.
The dutchboy and dike approach doesn't adress the underlying problem.