What is the phase response of SRRC/NRZ/RZ pulse shapping filters and does it matter?
FIR filters that have coefficients symmetric about their center coefficient(s) are linear phase.  Digital pulse filters commonly in use, including a Root-Raised-Cosine filter, are FIR and have this property, so they will have will have a linear phase response.

For all digital modulations, I would avoid non-linear phase response filters.