Actually the term "hate group" is defined as an organization that spreads harmful lies, falsehoods, untruths, ( whatever you want to call them), propaganda, false science, and partial facts or distortions in pursuit of their goals to denigrate, discriminate, diminish, and deny minority groups (such as GLBT+ among others) equality, rights, protections, and standing.
You (socal) seem to want to dilute the word "hate" because it seems you don't see the actions and speech of these groups as hate or perhaps even hateful. But they are. And the organizations are labeled and called out for it.
The "position" of traditional marriage (and that term has been shown to often have been much other than one man/one woman - if you've read lots of comments and responses in court testimonies, in blog comments citing many instances of situations that don't/didn't adhere to that simple one man/one woman description) may not itself be hate perhaps, but it doesn't stop there. There are actions those who advocate ONLY one man/one woman unions take to deny and exclude and vilify those who do want to join their loved one of the same gender in the same relationship their straight counterparts enjoy. Those actions and articles and campaigns are indeed hateful in tone, language, and results. And those "hate groups" deserve to be labeled and shown as such for their platforms, their actions, their harms.
Would that they were always announced on talk shows or in those two-minute "interviews" or "debates" of sound bytes on TV news programs with the preface "which has been labeled a hate group".