but the ends are brown shakes. Trim is a clay color.

The only brown I see is on the ground.

For the shutters, why not match the trim?

And a picture of the entire house will help with selection.

Ok. Thought we had kind of matched the trim but didn’t like it.

They out flat stones on the sides of the windows to make it easier to attach shutters. Some people like it as is, but I’m pretty sure I’m going to put shutters there too…..

I think a sage green would look good …

This is the wonderful Farrow and Ball Green Smoke:

If you’d like it a bit more formal, a very dark brown:

Matching the dark red/rust in your stone, love this:

This is Farrow and Ball London Clay, an amazing color that ticks all the coordination boxes … your stone, trim, shakes:

Your house colors are so neutral, you could do just about anything. :)

Some neighbors redid their house and installed shutters similar to the sample you show in your second picture. Theirs look dreadful - they look like broken-up wooden pallets (pallets like you would see under a stack of bagged mulch, for instance).

Your home is lovely. If you have to have shutters, get a more suitable, formal style.