Being Furry shouldn't have an impact on your religion. From a Christian Perspective, there's nothing wrong with being a Furry, it's the actions themselves. The Bible specifically says not to have sex with animals, but not all Furries do that. However, not all people who do that are furries. Therefore, being a furry isn't part of the equation of whether that's wrong or not.
Because of that ,anyone who says that being a furry is evil is wrong. At least, from my perspective. And if they're wrong, then it's simply because they decided to impose their beliefs, not what is in line with the christian religion.
This is another common example: People say that Christians have to love everyone and be friendly to everyone, not hold grudges, etc. The simple fact is, that's a lie. No one HAS to be nice to be a Christian. It's certainly recommended however as simply the best choice of action, but if you don't love everyone that doesn't mean that you aren't a Christian. It just means people don't think you are one. Same applies to Furries, same applies to Christian Death Metal music.