What about a bleach treatment and/or whitewash?

https://addisonswonderland.com/how-to-whitewash-wood-flooring/

https://www.remodelista.com/posts/scandi-whitewashed-floors-before-and-after/

Is your oak floor throughout the main level?

I've never liked wood floors in kitchens. I know it is all the rage right now but in the end it is susceptible to wear and it seriously limits your cabinet finish choices if you want natural wood cabinets(like you have) because you are stuck trying to make two different woods look good next to each other.

That being said, if you don't want to cut it out in favor of porcelain or some other flooring, there are plenty of options available to recolor it, but obviously the fancier the refinish the more $$ you will pay. I'd talk to a good refinisher first and see some samples of what they can do with red oak and what kind of $/sq ft you are talking for each option. You may find it is cheaper to demo your current wood floors and install a pre-finished new wood floor than to pay someone to do a complex refinish job with bleaching/staining/blonding/clearcoat/etc.

Thanks...... for your detailed information. Our hardwood floors are in the kitchen and eating area. We do not have a formal dining room. Carpet in family room and living room,

Curious what you ended up doing. I have a similar issue with Birch cabinet finished in a warm Gold Pecan stain and mate rub-on poly. Red oak floors throughout the house due to be refinished and I would prefer to stay light rather than do dark. I was about to post that same question...

Yes, 2 options. 1: minwax has a Pickled Oak and also a Simply White stain that lightens the red oak. The Simply White looks like a white wash. Option 2: stain first in a green stain (videos of it on pinterest), green subdues the red a lot making it look like white oak). Then stain again.