This is pretty clearly a "right to swing your fist ends at my nose" situation. If your parents aren't attempting to limit homosexuals' ability to live as equals with non-homosexual humans then, yes, they shouldn't be persecuted for their beliefs. However, if they donate to political causes that are anti-gay-marriage, or march in support of those who do, or sign petitions asking for the right to marry to be repealed...
If you're uncomfortable with associating the word "hate" with "against gay marriage", consider what opponents of gay marriage are trying to stop:
* A person easily being able to be present at the deathbed of their lifetime partner.
* Joint custody of children.
* Tax breaks.