The door is most likely Fir, whatever you put on it makes it darker. You could try using a two part Wood Bleach to remove the color of the wood. You may just be able to apply a several coats of wax to keep the color the way it looks now.

Ouch. That is a real nice clash going on there. Sorry that this didn't come up before you paid all that money. In essence you will be ADDING MORE to make this disappear. Like MORE area rugs than you can shake a stick at! And LOTS of art to pull the eye away from the striking colour clash. And the only other thing I can think of: YELLOW lighting. Yep. See if you can get rid of some of that gray/green in the kitchen flooring by ADDING yellow (warm) lighting to the space. The other thing to realize is all that pretty gray paint is causing the kitchen flooring to turn gray. And the answer to that is 'more paint'. Sigh....start with the lighting and go from there. All it is going to cost you is a package of "warm" bulbs. But be prepared to paint over the gray in the the kitchen.

Hehe. It's a beauty and you have to appreciate that the owners did what they did with furniture and not with the gutting you'd expect nowadays.

In your case, I would paint the trim white. Personally I am not a fan of wood trim unless it also ties into other elements, like built-ins. You can keep the wood on the French doors and closets, if you like that look. Me? I would paint it all white.