Is it required to engage afterburners during catapult launches from an aircraft carrier?
This answer mentions that afterburners are used for night takeoffs as per regulations, but not required during day takeoffs. Is this true? If yes, why?
The short answer is very much "no" -- afterburners are not at all required to launch from an aircraft carrier. Longer answer: Fred Larson's comment is correct: it really depends. Ultimately a given aircraft, at a given weight, with a given wind-over-the-deck, and a few other things, requires a given amount of thrust to get airborne -- whether it comes from dry thrust or afterburner doesn't change the requirement.
Current aircraft like the F/A-18 Hornet can be launched without afterburner in some, but not all, configurations. For the most part the incremental safety margin and increased take-off weight means that afterburners are used for takeoff, but it's not strictly a requirement.
It depends on the aircraft type, loadout, fuel aboard, required endspeed, weather and winds, etc. Some jet aircraft or carriers e.g. the S3 Viking, A-6/EA-6B, A-7 etc. did not use engines equipped with re-heat, so that was not an option. Earlier incarnations of the F-14 required the use of reheat during cat launches due to the low thrust and temperamental nature of the older TF-30 engines; when the GE F-110 powered F-14B and D variants arrived on ship they allowed for launch without the use of afterburning for most load outs and mission profiles as the newer F-110 engines had a max dry thrust on par with the TF-30’s downrated afterburning power output! The F-404 and F-414 have been solid and reliable power plants for the F-18 series fighters and usually don’t require the use of reheat for light loadouts. Again the flight crew will have to make that decision based on the factors described above.