For this kinda discussion, it is very easy to show bias as to say for example, "Character I like represents my side, and character I hate represents the side I think is LITERALLY HITLER!" Sadly though, I'll have to speak somewhat in stereotypes to make determining their political views easier.
For Twilight, it's pretty hard to determine if going by American politics. Yes, she values knowledge and science, but in America both political parties tend to only use science when convenient for their narrative, and outright ignore it when it goes against it. But if we stretch to other parties, definitely a monarchist. She is a princess and all.
Applejack would be conservative. She values hard work for the reward, which if we go by stereotypes, is what the conservative side tends to prefer. And if we're to take this stereotype farther, there was an episode where she wanted to stop a bunch of bats from mooching off her food, which you could easily replace with say an immigrant.
Which leads us to Fluttershy, who was on the opposite end of that thinking in that particular episode, making her liberal. She would also be an animal rights activist if in the real world seeing her love of animals. To top it off, in Equestria Girls, she was seen eating a veggie burger, making her either a vegetarian or vegan, which is what a stereotypical liberal would be.
Rainbow Dash and Rarity are both pretty hard to determine. Both don't really show any political bias in any episodes, as they're both more goal oriented with their respected hobbies. I guess both would be independents with Rarity leaning slightly to the left seeing as sometimes the fashion world can be associated with gay stuff.
And Pinkie would just create her own political party, with balloons, streamers, and cupcakes