You'll have to test different products to see what you are happiest with. I find General Finishes products high quality and easy to use. Minwax not so much. Here's their matte clear.

I'm not fond of Minwax (low grade stuff meant for DIYers who are unable/unwilling to pay for higher grade stuff) and I'm even less fond of a polyacrylic (I've yet to find one that is tough wearing). There's a reason very few PROFESSIONAL grade products (the one's that are more than $100/gallon) are polyacrylic.

And as ksc36 points out, if it does not SPECIFICALLY state "flooring" on the can/label, then it is most likely meant for furniture or trim (which Minwax does quite well with...simply because it is cheap, easy to find and does NOT need to be tough).

If you must use "off the shelf" stuff (because you are DIY and don't have access to a professional's tool kit/knowledge base) then work with Varathane Diamond Coat Floor Finish. It is tough and clear (no yellowing) and will do wonders for a stair tread. It should be $80/gallon. Go ahead and find the satin...or if possible a matte (but I don't remember seeing a matte in that line up).

If you are using a professional to do the work, get them to bring in Bona Traffic Naturale or Loba 2K Supra AT Satin. These are the BIG BOYS of the floor finishings world. They are magnificent products with magnificent wear characteristics and are non-yellowing.

Based upon another thread, who are you going to have apply the coating?

Mark, I am hiring a painter who has experience. I am not having the Builder do this. S he came over today to give me an estimate.

There is a trade off here. As you've stated the trafficked area of the tread will be covered with carpet. No one will be walking on the wood side areas. They are entirely decorative. For that reason their visual impact is 100% of the utility you're looking for. The finish I've suggested is aimed squarely at that end goal. By no means is it primarily a floor finish. It's a furniture finish not meant for the hard use of foot traffic. If it preserves the highest amount of the visual characteristics you are looking for it's meeting your primary intent. Try some of the harder General Finishes water based finishes in matte or flat for a harder finish. Enduro Conversion Varnish is one.

As already mentioned Bona Naturale' is a great product. You will need to have an experienced professional to apply but it will be worth it.

Is there a reason you don’t want it to match your floors?

Nini, I don't want the doors to be as dark as the floor. My house turned out way much darker than I expected with the California Blue Pine (a lot of it being dark blue) covering most of my cathedral ceiling. I'm trying to make up for that by having many things in my house light colored or white. It seems to be helping. It made me claustrophobic and overwhelmed before I did some of the white and light things.

Do the treads already have a finish on them? The newel post is raw oak, but the treads look different.

PPF, nothing has a finish on it yet. I see what you mean, but I haven't put anything on the stairs or the post yet.