Whether you should do a filter task yourself depends less on how hard it looks and more on what the task touches. A cartridge in a sink housing is a different job from a tank change on a whole-house system. Sort each task by the parts it disturbs, the water it can release and the warranty it might affect.
Tasks most homeowners can handle
Replacing a sediment or carbon cartridge in a standard canister housing usually involves closing the shutoff, relieving pressure, unscrewing the housing, checking the O-ring, seating the new cartridge and slowly reopening the water. Under-sink reverse osmosis pre-filters follow a similar pattern. Keep the manufacturer's instructions open, and do not force a housing that will not turn.
Tasks that touch the main line or the drain
Changing media in a whole-house tank, reconnecting a bypass, or altering the piping around a softener or whole-house system involves higher pressure, heavier parts and sometimes a drain connection. These are the points where a leak or a cross-connection can cause damage that is expensive to fix. Hire a licensed plumber or the installing company for these tasks.
Tasks that belong to the service technician
Control valve work, resin or media bed issues, sanitizing a system after service and any repair that requires opening a sealed tank are technician jobs. A technician also has the tools and test equipment to confirm the system is working afterward.
Check the manual and the warranty first
Some manufacturers allow owner replacement of cartridges but require professional installation for the tank or valve. Some warranties are void if the system is serviced by an unlicensed person. Read the owner's manual and the warranty before you open anything, and keep a record of what you changed and when.
Stop if the shutoff does not hold
If the shutoff valve drips, sticks or does not close fully, do not work downstream of it. Call a plumber to replace or repair the valve first. A filter swap is only as safe as the valve that controls the water.