Every single Fire Aspect enchant (lesser, Normal, advanced, and Supreme) on both the Living and Sentient weapons don't apply fire to the S&R Parasites, BUT Fiery Edge does ignite S&R Parasites.
Fire Aspect DOES work on every other weapon with S&R parasites. (as does Fiery edge) AND Fire Aspect DOES work on every other mob with Parasite Weapons.
Weirdly, wearing the "Fire Gauntlet" allows you to ignite parasites with a Fire Aspect on the Living and Sentient weapons.
Flame on the Living and Sentient bow works just fine.
What really hurts is Fiery Edge can't be used with Ash Destroyer, so you lose a lot of potential damage. Unless you bring another weapon to ignite the parasite mobs.
Also the affects of the Living and Sentient weapons don't do anything. The Scythe's "Sweep," Great Swords "Bleed," Cleavers "Virulent/Viral" strikes. Ect. (These affects work in RLCraft v2.9.3)
Things I tested/TLDR: ALL versions of "Fire Aspect" don't work on the Parasite weapons, specifically on the S&R Parasite mobs. Fire Aspect works fine everywhere else. No bugs with Fiery Edge.