Will a BPSK Demodulator designed for [ 0º , 180º ] symbols work for [ +60º , -60º ] symbols?
For 0/180, if you track the carrier (RF, IF) phase, you'll only need a single-phase local-phase reference.

For +60/-60, for optimal BER you'll need inphase and quadrature, so you set up matched filters with precise phasing. Keep in mind these are not orthogonal symbols.