Here’s the short answer:
Stop worrying about games changing you and take it for what it is. Undertale is a great game and while the majority of characters look like animal people, they are still not the focus of the game. It’s your journey in dealing with them that is the focus. So don’t worry about it. Did Pokemon make you a furry? Did Looney Toons make you a furry? Play the game.
Here’s my long answer:
I hate this question. Does liking X make me a furry?
I was going to get into a thing where I wanted to say being a furry has a lot to do with self-identity and that if you don’t identify as furry then you don’t have anything to worry about.
But sources tell me that the definition of being a furry means taking a liking to anthropomorphic characters. Which I think is dumb. That’s such a general definition. I don’t think there’s anything wrong with liking characters that happen to be nonhuman and i don’t think people should have to be labeled just because they’re fine with it.
But in terms of the game? The characters are not “furry” persay. Even the ones that are closest to animal people are just defined as monsters which is a term that could sum up any creature in the Underground. If you’re sexually attracted to any character nothuman, I’d be quicker to say that you’re more open minded than “a furry”.
I like the term Xenophile because that is a blanket term for “attracted to things different than you” which I can proudly say that I am. I’d fuck one of those lizard babes from Flash Gordan in a heartbeat. But being identified as a furry still annoys me. So even though my followers can totally say “You draw animal people all the time! You’re a furry!” I don’t feel the need to convince them I’m not because it’s just not a title I enjoy wearing or care about defending myself against. Same thing with Brony despite me having a lot of the traits of a common brony.
So no. If this game turns you into a “furry” then perhaps you had some underlying conflict within yourself and you might choose to blame the game, but it’s not the game. You like anthro butts. And that’s okay.