When installing sharkbite fittings you should leave the plastic in the sharkbite fittings otherwise it can damage the fitting and teeth inside the fitting.
The sharkbite fittings need the plastic liners inside them and plastic inside them to make a proper seal with the pipes you're connecting.
I've never removed the plastic inside the sharkbite fittings.
If you do remove the plastic from the sharkbite fittings then they might leak after you install them and then you'd have to put the plastic back inside the fitting and reinstall it.
The plastic inside the sharkbite fittings is there for a reason and to make it connect properly to Pex, PVC and other piping.