I'm looking for a varnish remover that will not dissolve the rubber butt pad or the glass (gel) bedding. Sandings is fine but I want to retain the checkering and still get the varnish out. Any specific products would be apprieciated.

I've had good luck with ZipStrip but I always take off the furniture first.

Try a little on the glassbedding in a place that makes no difference.

I use Laquer thinner (OUTSIDE!!!) to rinse the cleaned wood and a bronze dish scrubby thing to clean off the goo made by the remover.
(Its fun to tell the grocery clerk that dog/cat/bird/wife, etc ate the last pad.)

When I get rid of factory finish on my 10/22, I used methyl hydrate(methyl alcohol, poisonous, cause death/blindness if ingested, careful with vapor too!).

I spilled it on the gunstock liberally and wrap the entire wet stock in a big plastic sheet so the liquid doesn't dry out. Scrub the stock clean next day.

Never use acetone, it's expensive and ruins Acraglass.