Is it safe to replace a 15 amp GFCI outlet with a 20 amp GFCI outlet?

If the wiring is 12 awg it is safe.

I caution folks that want to upsize parts to check the wiring because sometimes a breaker was upsized to prevent un wanted tripping.

A 20 amp GFCI really doesn't provide any thing that a 15 amp will except the ability to plug in a 20 amp device. When was the last time you saw a 20 amp plug on an appliance? They are out there but rare and the 20 amp costs more. Note they both trip at ~5 ma fault current.