Accepting opinions and respecting people does not strip our ability to have our own views on the opinions and actions of people.
However, it is hard to accept what you do not understand. I am utterly bewildered by the fact that so many people oppose same-sex marriage, and that people truly believe allowing gays and lesbians to marry has any impact on them or their lives.
Calling the amendments banning gay marriage bigotry and hatred (which I truly believe they are) does not mean I am calling the people who voted for it bigots and haters. This is the same as being able to hate what your child does while still loving them with the entire depth of your being.
How are gay people getting married imposing their will on anyone else and impacting anyone else? Heterosexuals will still be able to do and be everything they can do or be today.
Since there is no impact or harm to those outside the marriage, people can disapprove of the gay marriage as much as they want (like what can happen with straight marriages), but there is no right to deny gays equal access to marriage.
People can hold all the values they want, but they have no business to restrict the rights of others because of it when they are not impacted by it.
