Is the F-16 capable of taking off during a nerve gas attack?
Source: Pilots Don MOPP Protective Gear - 25th Fighter Squadron, YouTube

If the base is equipped, then yes. The ground/flight personnel don the specialized suits for chemical/biological warfare.

And according to thedrive.com, a suit is also available for the F-35, though it took a decade to design. The delay was due to the F-35's complicated "enhanced man-machine interface".