What is the phase response of SRRC/NRZ/RZ pulse shapping filters and does it matter? So I would like to know if filters usually used for pulse shaping (like SRRC) have a linear phase response, and if not, what this response looks like and does it matters in any circumstances?
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.