The big monkey wrench in this line of questioning is Orson Scott Card. He might as well be a walking hyperbole. The guy sat on the board of directors for an anti-gay hate group for years. Just in case you thought his gays-are-pedophiles work was something he just did in his spare time outside of his writing work, he's recently gone and rewritten Hamlet so that Hamlet's father, and this isn't exaggeration, was a gay pedophile demon who molested most of the male cast in their childhood.
So to answer your questions:
1) Should a creator's political viewpoints have an effect on them being given awards - awards that ought to be given based upon the quality of the work itself?
In general, no. I'd like to see works based on the merit of their worth, not whether or not someone is a Republican or Pro-Choice. That being said there are the hyperbolic edge cases like I called out above. I don't think it would be out of bounds for an award to say, "You know what, no matter how good this book is, we probably don't want to be giving a platform to hate-group leaders." A little pragmatism now and then isn't always a bad thing.
2) Should a facet of someone's identity (race, sexuality, nationality, ect) have any relevance as to if their works deserve awards/good publicity?
Depends. If you're doing a no-restrictions, open to the public award show like the Hugos, someone's identity shouldn't factor into it. In light of the Hugos usually being super white and super male, I wouldn't have a problem with someone starting a women-of-SF or POC-of-SF award show. (In fact, I'd be amazed if these didn't exist already.) I'd even be alright with a book recommendation list of, "Authors from diverse backgrounds you might not have read". I don't have a problem with boosting underrepresented minority voices, a (fair) general merit based award is not the place to do it.
3) Did Gamergate have any actual effect on this - or are they being used as a boogeyman figure?
I don't exactly keep tabs on KiA, so I couldn't say. Being misattributed like this seems like an artifact of the group's loose organization and low barrier to entry. Unless Gamergate gets a clearer message and tighter membership policies, they're always probably going to be synonymous with "that weird anti-SJW part of the web".
4) If you're someone who allows an author's political stances, identity or presence on lists like this influence what you read (or add to your planned reading list), why?
There is an astonishing amount of Science Fiction being written out there. There's even an astonishing amount of good Science Fiction being written out there. At this point, I don't really care how great Ender's Game was, I'm not going to give any money or attention to the guy who thinks I'm a pedophile and is trying to take away my rights. This might not jive well with a let-the-work-speak-for-itself philosophy, but once again, I'm being pragmatic about the edge cases in this sort of argument.