BRC Issue 7 (and previously, FSSC 22000) certified plant here. We use electric forklifts in our production areas all the time. The production forklifts are segregated from the warehouse forklifts. Basically the same system as a captive shoe/uniform required area. The production area has two forklifts (one for the manufacturing side, one for the packaging side) and they stay within an area that is segregated by lines on the floor. They get their wheels sanitized/disinfected every week.
Deliveries from the warehouse to the production space are via warehouse forklift and warehouse racking. Warehouse forklift stacks materials in the racking from the warehouse side, the production forklift pulls it off the opposite side for use in the production area.
It's an attempt at separating the forklifts that enter and exit trailers and those used in manufacturing.
BTW, there are a few GFSI standards (perhaps all??) that require electric only forklifts in food handling and storage areas (no internal combustion).