There are a gajillion threads to read on this topic at Houzz. Just plug in "hardwood floor finish" or similar and search under advice. But yes there are other options besides polyurethane. Search online for Hardwax oil finishes or check out the oft referred to Rubio Monocoat in this forum. And there are a couple of different pros here that likely will weigh in shortly: Cancork Flooring and Ultimate Hardwood.

Polyurethane is still one of the most popular and most understood product. It is still found as a solvent based product (read: "oil based"...customers didn't like the word "solvent" so they changed it to "oil" to make it sound better = no change in formulation; just a name change). For those who do not like the VOC content of solvent based products (or those people who live in California) the water based products are now performing the same or better than the original solvents.

Not all polyurethane is created equal. Solvents = strong yellowing/ambering with heavy odours and long cure times. High end water based products have Zero yellowing with very little smell and fast cure times. Oil modified (solvent based products that have a lower solvent content) will yellow a bit have some smell and have medium to long cure times.

Hardwax or oil finishes (not to be confused with oil based polyurethane) are a fast, convenient finish that have very little odour and cure quickly (5 days). They are natural "matte" finishes (very low gloss) that require a bit of homeowner up keep...but they can be done by the homeowner....no professionals needed.

The polyurethane/urethane/resin finishes come in "ultra matte" through to "super gloss". The "super gloss" and "gloss" are the "gymnasium" finishes you are worried about. The lower the gloss level, the less likely you are to have your floor look like a gymnasium. Satin is very common.

The oil/solvent based polyurethanes are what "Joe the floor guy" will know and understand. If you wish to work with "something else", you will need to work with someone OTHER THAN "Joe". For a different finish, you will need to work with some trained in the product you choose. Do not ask an "solvent based poly" finisher to try his luck at a European 2 part water based polyurethane....you will be in tears and he will walk away from the job before it is 1/2 finished.

Match the professional to the finish you want. Anything else is trouble.