My bandmate and I each have a Fender Deville 410, and some pedals that support stereo output. Since the amplifier has two inputs, is it possible (more importantly, safe) for us to be both plugged into both amps (I would be plugged into Input #1 of mine, and #2 of his, and vice versa for him) so we could both use stereo effects?

Ideally we would be playing through only our own amplifiers, until we wanted to take advantage of the stereo for a delay/mod effect or something.

I've heard differing opinions about whether or not it's safe for two guitars to be playing into the Deville at the same time, but most say it's ok.
That's perfectly fine. I've used both inputs a of a two-input amp before. It would be better if you had true two-channel amps, like old Bassmen or Twin Reverbs, but it should be okay.
It will work, but your tone and his will blend together and it won't sound that great really. Generally when using 2 inputs on one amp, one of the signals will come out quite a bit louder than the other.