The theory tells that if BFD stops to receive keepalives, it informs to the routing protocols that the neihgbor is down. If I configure BFD only in one side and associate BFD with the routing protocol, the neighborship goes down?
You need BFD on both side but you could use echo mode on one side only.
I tested it with 12.2(33)SRC2, and configuring BFD on one side only doesn't bring down the IGP adj. The BFD session stays in AdminDown state.