If I were to use RemoteEvents and RemoteFunctions would the script work fine even when FE isn't active?
Yes, they will.
Possible scenario where an FE script isn't backwards compatible: Say for instance they are making local parts by inserting them into the workplace.
Generally, if you want to make a part local (only you can see it) then you need to create a part with a local script and put it into the camera. This works with FE on or off.
If FE is on, technically you can just change something in the workspace and it will change only for you, but if you want backwards compatibility use the camera method, although I will say it is better in general to Just use FE.
Yes, FilteringEnabled designed scripts or system will work when it is not enabled.