Quarry tiles are what is often used in commercial kitchens and I suppose the grout can appear to be Portland Cement.

Just like you can stain concrete you can stain the grout, but it will be time consuming .

https://www.groutshields.com/index.php/blog/tag/grout-stain/

https://www.todayshomeowner.com/video/staining-grout-lines-in-tile-floors/

you can also try GroutRenew to recolor the lines. it's slow going, but it will work. test in an 'off' spot to see if it colors the quarry tile too. if it does, you'll have to be very careful, or try sealing only the red parts of the floor. you can try doing a darker gray, but these tiles were meant to have the lighter grout.

you could also use a tool to grind down half of what's there, and grout in a color that matches.

What you have is a classic mud set tile installation that will last longer than the house will if you don’t futz around with it and ruin it. Things that are classic do not need “updating”. That’s a dirty word for an old house. It’s usually the equivalent to remuddle.

That's the flooring I laid in my 70s Deck Built modern house 35 years ago. Looked just like that.

Thanks, guys! Sophie, I agree with your point. I really don't want to do something to "remuddle," it's rock solid! I forgot to mention in my OP, though, that this is a space I'd like to use as a formal dining room, and I feel like the color of the tiles/ mud will be somewhat distracting from the ambiance.

I'm with you Beth...rug is a must!

I was impressed by how perfectly spaced the tiles are installed. Lots of postings here re: poor tiling installation, uneven grouting, etc. It’s nice to see a good one for a change. Get a large rug. Also rug cleaners in my area offer service of steam cleaning grout. Not prohibitive and flooring looks like new. You might want to ck into that.