The shutters read brown on my monitor, but it could be the light in the photo, which I think it probably really oranging the brick, too? If you wanted to leave the shutters as is, I might try a teal or turquoise door, but I happen to love that color with brick. I picked this photo when I thought your shutters were brown. I found this of the garage doors painted the same color as the siding (although different color than yours) and like how it looks with no trim. I also think this is a great color with the brick, but probably not with your siding (unless you'll be painting that, too). I like the darker trim color with it all. This is from an older GW thread, so I hope the OP doesn't mind GW thread

I'm no expert but I think you're right, you probably want to keep the garage door matched closely to the brick around it so you don't highlight the garage. I think the bright white on the front door looks nice but maybe to make to stand out more a different color would be fun, but yeah, not red, lol! Ok, I'm no help but hopefully my comment will bump it up.

Snap a photo on a sunny day then use the Sherwin Williams ColorSnap app to play with the colors. I would select a tone slightly darker than your mortar for the garage door and a color slightly darker than your darkest brick for the front door. I would then on the garage door install magnetic faux hinges and windows; this will add detail to the door, like the below house. I know they can be found on Amazon, not sure where else. Before: After:

Good point about the garage doors fading away. When I bought my house they were a contrasting color. Once I painted them the same color as the body of the house, the house seemed much larger. Also, the front porch was more prominent. I think if you do this for your house, then your very lovely front porch will become the focal point. Right now, it competes with the garage doors. So i recommend painting the garage doors a color that is very much like your brick and selecting a color for the front door to make it pop.