Both FET and RET share their views on mass. So special relativity applies.
However it is their view on weight that differs. Whilst both agree on the figure, the phenomenon that causes weight is disagreed upon. Gravity/UA.
RET says mass causes gravity, FET says gravity doesn't exist.
Actually in some factions of FET, gravity very much exists, but I do not want to fragment the thread.
For the sake of UA theory it does not exist.
Whilst mass does not cause gravity with UA theory, mass is still there. Mass after all is Density x Volume. Things still have both a density and a volume in FE. It is just that this mass does not create a magical force, attracting all else to it.
One is not reliant on the other. Both theories enjoy the property of mass. How a mass is given weight is the dividing point. UA/Gravity.