A vote to paint the shutters white to match the rest of the trim -- and then wait to see if that change will affect the decision to change the color of the front door ...

Thank you for the response! I like the idea of white but wasn't sure if it would blend in with the siding too much (or make the siding look dingy in comparison).

I like the blue shutters. You could also go with a darker green.

You already have the white round vent above the windows -- and the white trimmed porch as well as the white fencing -- so the white shutters would actually blend in with those elements ....and if the shutters are painted white -- then the windows themselves would appear to be larger and more visually cohesive to the viewer's eye ....

And I guess white shutters would make a more neutral palette so I would open myself up to more door color options :-)