I have some piping systems that are Category M Fluid Service, 2" and below. The temperatures will be near ambient and pressures less than 150 psi.

Should the pipe supports we use attempt to make the pipe system more rigid or more flexible to better meet seismic conditions?

Supports with higher stiffness will give higher eigenvalues.
Look your spectrum. See the highest acceleration beginn with frequency and end frequency.
Higher earthquake acceleration normaly at about 3 until 8 Hz.
Example :
You have a very low stiffness pipe about 2 Hz and make the supports stiffer,then this eigenvalue will be > 2 Hz and can fall in resonanz
( higher acceleration in spectrum ).
But if your eigenvalue 7 Hz and you make your supports stiffer, then your eigenvalue will > 7 Hz and can go out resonanz with lower dynamic results.