Yes, of course you remove and trash gloves to avoid contamination. I did biochemistry for years. We wore gloves to protect proteins in samples from our proteases, and to protect ourselves from radionuclides. When I labeled stuff with mCi levels of I-125, I worked in a fume hood, behind lead bricks, wearing a lead apron, and three layers of PVC gloves.
But I always tossed the gloves before leaving the work area. And usually I'd put on fresh gloves before removing the lead apron.
That wouldn't be workable day to day. You'd probably go through 50-100 gloves per day, doing it right.
