Becoming a furry is a slow ease into the community. Despite being one for nearly a year now, I still can't stand the thought of wearing a fursuit, despite being ok with others wearing one as well. Just slowly expose yourself to furry things, at your own pace, and your mind will (hopefully) adjust to the new concept.
If it's a genuine fear of yours, it can be resolved in a similar way. People are less afraid of something the more it happens (unless it's caused trauma of some kind).