Varnish, the non poly kind. One type is in the link.

Oil based finishes do add an amber tint, but most folks like that effect.

Here is a link that might be useful: Sherwin Williams varnish

Varnishes are all "poly" something; I think it is inherent in the definition of varnish that they harden by polymerization. The polymers may be phenolic, alkyd, or urethanes. All are relatively tough film-forming finishes, which is what I would use on a door. The differences among the different types are much smaller than the similarities. Unlike Handymac (who I assume means polyurethane when he refers to "poly") I would choose an oil-base polyurethane for an older door to get the look of an oil-based finish and the best wear resistance. Other varnishes will also work well and be more historically appropriate. If your woodwork is to be gently used, shellac could also be a nice choice, a lot of woodwork of that era was done in shellac, one of the more amber grades. It has the advantage of being easily repairable.

What I meant(and what is accustomed in the finish industry) is a varnish without polyurethane. Polyurethane is a form of plastic. It does form an very hard finish, but the resultant finish is subject to chipping. The chips are actually pieces of the finish that are missing.

Polyurethane finishes are not easily repaired, the normal repair is to sand and completely recoat.

Non poly varnish can be spot repaired by sanding the area needing repair and feathering on new finish, rather than the entire piece.

For high use applications like cabinet doors, using polyurethane finishes can result in the ugly chipping and difficult fixes.

Not nearly the same issue with non polyurethane finishes.

Shellac is a wonderful finish, but not good in high moisture areas like bath/kitchen areas.

Thank you both for the great input! I really want to do these beautiful doors justice.

Being ever the pedant, I can't stop myself from pointing out that traditional varnishes are also "plastic". (I'll try to stop now)

I don't think I've ever seen this chipping phenomenon with polyurethane, though I could imagine it with a thick coat. I have seen that sort of thing with thickly applied shellac, where it shatters on impact. I suppose it would be a property of any finish that is brittle when cured. I keep my polyurethane coats very thin; I can imagine a thick finish layer of any sort could be subject to all kinds of problems like that.

Personally, I love tung oil as a finish. Its relatively small molecule sinks into the wood well and enhances the grain, and it doesn't add much yellow tone to the color, though there is a small amount. Chestnut has a fair amount of color to begin with, though, and so I don't think it would effect it much. You can use steel wool or a hard wax such as Renaissance Wax to change the amount of gloss to the finish. IME, I haven't seen chipping with tung oil, but that doesn't mean it isn't possible.

I know I am sounding like a broken record, but there is a difference between polyurethane finish and the original varnish finish.

Polyurethane

Essentially a plastic in the form of a liquid until it dries, polyurethane is available in both water- and oil-based options, and comes in varieties from satin to glossy.

Varnish

The name of this finish often is used generically for a finish or top coat. It's very durable because it contains a higher ratio of solids.

Here is a link that might be useful: Difference between polyurethane and varnish