Normally these are quite complementary woods and go together just fine when used this way. It would be very unusual, and a little odd to have the trim and floor be the same. What's not working?

You don't think the red oak clashes with the floors? I'm worried that once I'll put a clear coat on it it will look orange, and will not go with grey floors

Unstained white oak is typically a yellow/amber color and red oak a little redder. The grain differences are typically as or more pronounced than the color differences; have your floors been treated to make them gray?

Best advice is to finish some sample pieces of both in the intended way and see how they look next to each other before proceeding to the entire room.

The floors are prefinished and I have no clue what was done, though it looks as of colors were layered, root was glazed. But I'm. It sure.

Do you mean that the grain is very different in the two types of wood? If so I was afraid of that, I'm not a fan of the red oak gran....:( it looks so 80's is this even avoidable?

I have always found gray stain makes my oak projects look pink. Like the 80s pink oak. I end up putting a dark stain on it, which gives my projects a great, aged/weathered look.

I don't think your elements look bad together at all. Perhaps staining them with a similar color? But that is a lot of work.