Is BBY40 a good substitute for MV209 in this RF receiver?
Yes. BBY40 looks pretty close. It's within spitting distance of the same capacitance at 3v and 25v, so go for it. It has the same max reverse voltage, so if the circuit doesn't damage the 209, it won't damage the BBY40. It has better leakage, and a specified series resistance, so as good or better all round.

Why a varactor rather than a trimmercap ? You can adjust it with the covers on, or remotely, without needing a screwdriver, or even automatically in an AFC loop. You could mount the voltage control pot on the front panel, and there's your tuning knob, with none of the pulleys and strings that you had in the old radios. It's smaller, cheaper, and more robust, so will survive washing.