This is a complicated issue because technically with regard to the transponder there are areas where it is not required under 91.215(b), namely Class G and certain altitudes and places in Class E.
However, in the same section in subpart (c) of 91.215 it says
"... or in all controlled airspace, each person operating an aircraft
equipped with an operable ATC transponder maintained in accordance
with 91.413 shall operate the transponder."
So subsection (c) puts you right back at if you got it you have to use it. Unless its inoperable or if it was not inspected within the preceding 24 calendar months in accordance with 91.413, then you are prohibited from using the transponder.
To complicate matters now we have ADS-B Out requirement under FAR 91.225(f) which states
"...each person operating an aircraft equipped with ADS-B Out must
operate this equipment in the transmit mode at all times...."
The reason this is important is that many installations transmit ADS-B Out information through the transponder, so if the transponder is turned off, you will not be able to comply with FAR 91.225(f).
There are two ways to transmit ADS-B Out information, one is 978UAT and the other is 1090ES. I believe 1090ES is the method that uses Mode S Extended Squitter transponders and if this is the method your aircraft uses, turning off the transponder may turn off the ADS-B Out information in violation of 91.225(f).