You can always write in your candidate of choice.
Marriage isn't a right, it is a privilege which the society one is in grants or doesn't, just like obtaining a driver's license and keeping one is a privilege granted by the society in which one lives. Most things people like to call rights are actually privileges, they've just constantly had them without much hassle that they tend to feel they are supposed to have them rather than that they have to earn them or be given them. So, in answer to your second question, the answer is no. You aren't being denied the right, you are being denied the privilege. Maybe if people attacked the issue that way then they would make more progress.
BTW What I wrote only applies to legal marriage. Anyone or anything can marry anyone or anything else at anytime, usually. Depending on the society in which they live, however, that marriage might not be considered a legal marriage and so that society may not recognize it as a marriage in those terms. So if you wish the marriage to be legal, then you need to be granted the privilege by the society in which you live. There are some societies, though, where conducting a marriage ceremony, whether legally binding or not, is illegal in that society.