Perhaps an oversimplification - the Presidency is a crappy job, but many people simply aspire to positions of authority, of which this is one of the pinnacles. The best candidate is one who does it from the motivation of civic duty, and such a candidate obviously has to pursue it at some level. Pursuit of the position, for the right reason, should not be an automatic negative.
There is certainly a case to be made regarding the distinction between simple service and participation. One should probably not be required to participate in a private event that one disagrees with or finds distasteful.
I think that they are only trying to appropriate the rights and benefits that are accorded to the institution of marriage. The fact, that in a secular country civil marriage has become intimately convolved with the religious meaning, is hardly their fault.
That's the problem, in a nutshell. Legislative precedent says that we draw the line at businesses refusing to serve demographic classes. Arguing to move that line is fine, but may lead to the slippery slope back to widespread discrimination based on race, religion, gender or any number of other characteristics that the civil rights movement spent decades fighting.
Provided that you have no problem with busineses refusing to serve Christians, then your argument is, at least, consistent. But, under current law, that would be illegal, and hence so is refusing to serve other groups, whether religious or sex/gender based.
And your point is arguably disingenuous at best. Aside from the fact that counting state outcomes, especially when not all states put it to a popular vote, does not permit any conclusion on the national level of popular support, virtually all polls in recent years indicate clear popular support for gay marriage. http://en.wikipedia.org/wiki/Public_opinion_of_same-sex_marriage_in_the_United_States