Whether they are white or red, I'm guessing they are a lower-grade wood because of the random colorations.

https://hardwoodfloorsoak.com/grades/

• Like all domestic species, solid Oak flooring is given one of several grades: Select & Better, #1 Common, #2 Common, #3 Common (also known asUtility or Cabin Grade), and Character. While all Oak flooring has the same qualities, the grade it is assigned per standards governed by theNational Wood Flooring Association(NWFA) indicates its appearance. As such, an even appearance receives a higher grade, while hardwood with character marks or color variation is marked lower.
• Select & Better Oak flooringis primarily heartwood and has a uniform color. Select Oak flooring also contains more sapwood than lower grades.
• Moving down the grading scale,#1 Commonflooring, on the other hand, retains some of these qualities but may start to display a small amount of character marks.
• #1 Common, #2 Common, andCharacterfloors also have more color variation, including streaking and knots.
• If a floor that displays an overall even appearance is your preference, consider going with aWhite OakorRed OakSelect & Better floor.
• Keep in mind that, regardless of the amount of character marks Oak hardwood has, each species has a general set of qualities.

Check out this blog. This stain might work for your flooring.

https://www.chrislovesjulia.com/the-stain-we-decided-on-for-our-white-oak-floors/

For those who will ask, our contractor used the Duraseal Weathered Oak Quick Coat Stain (2 coats!), finished with Bona Traffic HD Satin. Deciding on a satin finish vs. a matte finish is definitely contributing to these floors looking like they’ve always been here–the goal all along.

It's character grade white oak.

Looks white oak. I do not see any of the colouring to indicate red oak.

G & S Floor Service… is there anything I can do to help hide the character?

Do you want to stain it darker, in an effort to reduce the difference in shades? Or do you want just a clear coat over it?

RedRyder. I love how it is now as the variations in shades and grain do not pop out at me but I’m concerned if I add a clear coat it will look yellow. I’m open to staining it a light brown shade, I want to avoid a dark stain in an effort to keep the rooms looking larger. 😅

@Beth H is an expert on doing a floor in a clear finish. Let’s hope she comes onto this thread.

Your idea sounds perfect to me and I’m sure standard polyurethane would do the exact wrong thing.

This could help. Bona Red Out anyone? (houzz.com)

You would need to stain it dark like dark walnut, antique brown or jacobean. Of course, water pop first.

If, you want to hide it completely. Apply a dye for a base color, then your stain of choice.

G & S Floor Service could you elaborate on what you mean by applying a dye for a base color?

Aniline dye is a different type of colorant compared to your traditional stains. It is available in powder and liquid form. Both are water or alcohol soluble. For large interior work, water soluble dyes are usually used. Transtint and General finishes are popular brands for dyes. You control the intensity of the colorant by how much you mix. Although best to stick to the recommended amount.

Aniline dyes are commonly used as a base color since dyes will not mix in with oil products, such as oil stains, hard wax oils and penetrating oils. Instead, you would layer these products over the aniline dyes for a more unique and custom look. The dye actually benefits from stain layering, since some are color fast - fade.

You can use dyes to achieve a undertone or use it to make a stain more dense. This helps with hiding unwanted characters and stains.

Example of a undertone use : Les Paul starburst guitar (color rings along the perimeter of the guitar)

Example of dense stain use : Espresso colored furniture (Super dark brown and black furniture trend was around 2008, some are still used today)

Some great expert advice from G & S