No, Folding has no adware/spyware. Either whatever spyware tool you are using is mistakenly labeling Folding as spyware, or the spyware came from another source. Folding@home is a non-profit organization. They have no need, reason, or want to put spyware in it.
Red Hat, yea, I had it running with Wine on my old Athlon. Apparently the Windows app on Wine is faster than the native Linux port of it.