Unfortunately for some, yes, it is important. But I still think you can be introverted and 'fit in' with your colleagues, or at very least have them like you. If you let them get to know you a bit and vice versa, if you show that you are willing to become part of the team socially as well as within work, it will improve overall feeling in the 'office' and you are more likely to be treated well in the case of any incidents or issues.
I respect people that keep to themselves to a point, but I think within an environment in which the norm is to at least have a chat with the colleagues now and then, 'keep to oneself' comes across as quite haughty and snobby rather than anything else. Sure, that's not intentional and thus unfair, however that is certainly what I've found a lot of people think. It's best to just give it a go, don't judge the colleagues just because they are social butterflies or you may not be, simply be friendly and offer some of yourself to the 'mix' of personalities at work.