Per the subject line, I don't think we addressed material changes.

Generally, material changes for fittings are unnecessary while the material properties for fitting and pipe are similar. Much of the time, the material properties are identical, but the callout for the material advises of different manufacturing methods.

If the fittings are wildly different materials, say fiberglass pipe and metallic tees, you will definitely want to encode those differences, especially if their lengths are comparable to each other. However, wildly different metallic materials is uncommon and impractical due to issues unrelated to stress.

With regards to whether or not you should model your fitting as a rigid element, you should ask yourself if the thickness of the fitting is approximately 10x that of the pipe, or if the stiffness of the fitting is approximately that of a pipe 10x the thickness. Enabling rigid element literally computes the displacement this way. However, if you do this, you must also be cognizant that you're also saying there's no way the tees themselves can fail. Calculated stresses for rigid elements will always be 0.