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that are anti-gay-marriage, or march in support of those who do, or sign petitions asking for the right to marry to be repealed...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.
Well, no. That's not what people who are against gay marriage are trying to stop.
Those are all different issues, and you'll find different percentages of people for and against each of them. Lowest against the deathbed issue, highest on the child custody issue, for example. Then the concept of redefining the term "marriage", which is yet another different issue.
Conflating all these issues is not helpful in the discussion. People's feelings on these topics are complex, and you really have to talk about it with that complexity to have any meaningful insight.
You may be right that supporters of Prop 8 wished to deny those benefits (hospital visit rights, joint custody, tax bracket, community property), but Prop 8 itself did none of the above. Gays (but not straight couples, at least until age 62) could enter into domestic partnerships that provide all the same benefits as far as the state is concerned. Regardless of Prop 8, gay couples wouldn’t get the federal joint filing due to DOMA at the time. Prop 8 was not about those other rights, it was about the words “marriage” and “spouse”.
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.