You may have a particular issue you have dear to your heart, and I accept that, but you have to have other people see your point of view rather then fear your point of view.
He didn't position himself as a threat to white people, especially white men, to the degree that he did to minorities, the LBGT community, and other groups.
Here's a good summary of his position on the topic: http://www.politifact.com/new-york/statements/2016/aug/14/se...
In addition, Pence has a history of anti-LGBT behavior as well.
When taken in consideration of how much leeway to decide domestic policy that Trump has promised to give him, Pence is a seriously scary VP for queer people everywhere in the US.
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[1]: http://web.archive.org/web/20010408125427/http://mikepence.c...
Trump's answers in those interviews don't sound much different from the ones we heard from Hillary or Obama back when they could not favor gay marriage either --but they've moved on and it looks like Trump has moved on (still, what he might do as policy is unknown, for now).
Just because you win an election doesn't mean suddenly everyone is forced to agree with your odious views.
The way forward for them is to protest and point out the flaws in the Trump policies and his presidency. To pressure the electorate and politicians that, no we aren't on board with a radical conservative restructuring of our society. Don't expect to suppress dissent with some kind of bullshit "respect the office" argument. Democracies thrive on disagreement and political change. These people are engaging in their right to self-assembly and protest. It will not go away. Trump supporters will need to deal with this. Its clear that you're trying to legitimize a novelty protest vote via this kind of 'concern troll' attitude and it just won't work. People aren't going to suddenly roll with the Trump agenda because you want everyone to play nice.
I think you have to realize that political change isn't about winning one election. The process involves and endless push back via many mechanisms, including protest.