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Pictures from further away would help visualize the combo better. Context is everything in design. In any case, I'd wait until the painted cabinets were installed before committing to a backsplash.

The cabinets are oak and will be painted to coordinate. Either shiitake with lighter tile or creamish with darker tile. I want to do the backsplash first and painting the cabinets will be sometime next year.

I prefer the lighter color with matching grout.

You should not do the backsplash first. Everything will look different when the cabinets are painted, and if you've installed your backsplash already, odds are it will not look right. I promise you.

So many different opinions on this. I had a color specialists tell me counter and tile first and then choose cabinet color.

It's hard to pick paint color last because it looks so different in different spaces & lighting. I guess my advise would be to start with what is most important to you & you can build around it.

“I had a color specialists tell me counter and tile first and then choose cabinet color.”

Whether cabinet color or counter color comes first is more individual preference - sometimes you fall in love with a certain counter so that the cabinet color would be governed by that. Or sometimes you know from the getgo you want e.g. cherry cabinets, or navy blue cabinets, white cabinets, etc. so then the counter choice is second to that cabinet finish preference. HOWEVER, the backsplash tile choice must be last, after everything is installed. Your kitchen will look quite different after everything is installed. There are so many posts on this forum from people who installed the backsplash tile too soon and realized they’d made the wrong choice. The tile did not go at all and did not look how they thought it would .

I don’t feel it will matter too much. So many paint colors to choose from.

I agree, if you are painting the cabinets and not picking an actual cabinet finish, there are dozens of variations of paint colors within the same general tones and levels of saturation, but a tile you like maybe only come in a couple of shades you like. Because you are open to final paint selection it will work to match the tile to the countertop and then to match the paint to that. If you were buying a manufactured door the order might be different.

Also put white paper or posterboard over the greenboard or prime the greenboard. It is skewing how anything looks.