I think the key is - both sides need to make an equal contribution. They should both get something out of the friendship - relationships where one person feels sorry for the other aren't going to be sustainable long-term, however well-intentioned. Friendship, like marriage, has to have a selfish element at its core - you have to feel that there's something in it for you, not just that you are being kind and fulfilling someone else's needs.
Obviously shared interests can be important, but I would say shared values are more important than that. I wouldn't match with a tick-list of hobbies with my closest friends but we have a mutual understanding and respect, similar sense of humour (very important!) and are likely to react in the same way to eg news stories.
I'm a vegetarian, centrist politically, love classical music, art and literature and don't enjoy sport (but I am very active and do lots of walking and swimming). I don't enjoy drinking (almost teetotal, in effect), I'm a lark rather than an owl, am sociable but not gregarious and know nothing of contemporary pop music or street culture.
My closest friends all enjoy meat, love their sport and vary from Tory to Labour in their voting habits. They prefer pop music and one is big boozer who likes to party! We would never have been matched on any kind of 'dating site' but we get on like a house on fire because we value and respect each other's differences.