I think they are people worried about the dangers of a Trump presidency in regards to foreign affairs. So with good reason they would prefer someone they view as awful replacing him because they know at least Pence wouldnt start a nuclear armegeddeon, something one cannot be sure about with Trump.
And the US isnt Indiana, not like Pence will be able to do a lot to harm LBGT rights compared to what Trump xould do to seriously threaten the saftey of the US. So how do I think about someone who places the safety of the nation and world.over some small threat to LBGT rights? Sane.
Pence's foreign policy goals are largely the same as Donald Trump's, and Pence's domestic policy goals are arguably worse. so no, it isn't just about LGBT rights.