Tough to tell much anything color wise from a pic 3" away. Step back and give us a wider shot please.

Here are more photos of the shower.

Fwiw, I think it looks good as is and wouldn't bother recolouring the grout for a few years still. Your tiled walls read as white to me. The grout pattern is subtle. When I told the tile showroom consultant I wanted white shower tiles, she advised me to go with an off-white grout, not bright white. The tile's "shadow" colour, in her words, which is often a very light grey. I used a grout pen in my old bathrooms to brighten up the old beige grout. Tedious but rewarding job. So far so good on shower walls (over a year). Recently did the floors - don't know how long that will last.

I think it looks great as is.

Thanks for the feedback, but it still looks dirty to me. I fee like I want to clean it but it is brand new and cleaning will not help. I am looking for more feedback from people who have stained their grout and how well it worked.