Facebook's structural problem
Now if you want to use Facebook to connect with new people all over the world on the basis of a shared interest, obviously this aspect is a bit of an obstacle. If your current Facebook friends don't share your interests -- and often they don't, since they're usually relatives, work colleagues and old school mates -- how are you going to friend new people who do?
Numerous groups for every interest
That's where Facebook groups come in. There are numerous active ones on just about any subject you can name. If you join many of them and interact with lots of different people, you're sure to find some you feel a sense of rapport with. Then after a little while you can send them a friend request.
They are much more likely to accept than if they had no idea who you were. By doing this you won't risk getting your account blocked. But it's still a good idea to only send these requests out occasionally. (You can also use this approach with Linkedin. The groups there are an excellent way to get on the radar of lots of new people then make connections with them afterwards.)
Create and use lists
As you build your network of friends on Facebook you can create lists for different interests. So if you have a blog post about blogging, for instance, you can share it with that list only. You're sure to get a good proportion of your network clicking on it.
If you have a Facebook page for an interest that you want to start promoting, you can send those friends who share it a request to like it. Again, since you've preselected them on the basis of their interest, and also got to know them a little, they are much more likely to agree to the request.
This method can be useful, particularly if you've only just started a new Facebook page. After all, it can be hard going getting those likes at the beginning, particularly if it's in a saturated niche.