The project is an oak dining table top. The varnish had worn off in spots. After stripping a few spots that had been exposed for longer still had a gray, aged look. It is a veneer so I didn't want to do too much sanding; therefore, I used Bar Keeper's Friend (oxalic acid) to bleach the spots. That and light sanding lessened the stains enough that I moved on to staining after cleaning the entire table with mineral spirits. Used Minwax penetrating stain and it looked beautiful. The "problem" occurred when I applied Minwax wipe-on poly. The first application dried fine, except for the spots where I had used the bleaching solution. Those spots stayed tacky. After letting it sit overnight they seemed sufficiently dry to apply second coat. But the tacky feel is again present only in those spots. I am considering trying a shellac finish over the poly. Other options y'all might suggest? Any advice on how to proceed is much appreciated.
Your best option at this point is to adopt a wait-and-see attitude, so just wait longer and see if the varnish will dry properly given enough time.
Be patient. Sometimes drying is slowed by one or more factors and sometimes it's slowed a lot, but often (usually?) it will cure if you can just wait it out. Many times when you read someone complain that their varnish "just wouldn't dry" you find out they only waited a few days to a week, when in my experience retarded drying might take weeks to resolve.
However that is not to say that drying will always complete, unfortunately it is possible to have something that remains permanently tacky :-( And in this case the best course of action is often to strip back and begin again*.
For now, if you can, put the table somewhere warm with good airflow to provide the best drying conditions.
I am considering trying a shellac finish over the poly.
That would work to seal off the areas of new varnish, but it would be best to apply the shellac to varnish that is dry to the touch because otherwise the tacky surface could interfere with application — you'd have 'draggy' spots.
And in order to have a varnish-tough surface you'd need to apply further coats of wipe-on over the top, the shellac then being used as a barrier coat (something it is often relied upon for).
If you create a new surface of shellac it'll be like you only applied shellac, your tabletop will remain permanently sensitive to water, will be damaged by alcohol, and won't be as resistant to scratching as you'd like it to be.
*Although if it's very slight a coat of paste wax over the top can resolve the issue enough that the surface is usable. But be aware the tackiness indicates the varnish hasn't dried thoroughly so the surface won't be as tough as it could be.