Can't reliably transfer over serial connection between two PICs

[richard]

I have series of 16 APA102C leds connected to the same 1936

is that the same 1936 that

The receiver (1936) which runs MIBAM, does nothing besides BAMing and checking serial input, if anything is delivered.
"Anything" is delivered in form of single byte, once per second, minute or hour.

So if MIBAM is messing with SERIN2, it should mess with SHIFTOUT as well?

sort of, the timing will be screwed up but since the pic is master and clocking is synchronous it won't matter the apa102c's are slaved to the masters clock.
pbp has shiftin and shiftout commands but they both act as master, there is no shiftin slave mode command.
any bit-banged reception code you make would need to honour the synchronous nature of the protocol i.e. interrupts will be a problem

there is a reason hardware peripherals exist.