I wouldn't let the neighbor's door stop me. Lots of people have red doors. If you don't get responses here, try posting on the Home Decorating forum.

If you make the other changes as suggested, I don't think you'll feel the need to paint the brick. There's no sense creating a maintenance issue where there is none now. The house has the potential to be very handsome. Some pretty pots with flowers on either side of your door will add some color as well. Don't forget that nothing looks pretty this time of year when trees are bare and lawns are brown.

Be aware that most folks here despise decorative shutters that are too skinny for the Windows and refer to them as "shudders". It doesn't matter if your home was built with them. Consider adding wider trim to all of the windows. If budget allows, consider a portico for the entryway. Paint scheme & portico:https://binladenseahunt.com/home-design-makeover-level-46/home-design-makeover-level-46-bi-level-house-exterior-renovations-google-search/

I would go with a medium to dark blue, or a bronze (like Urbane Bronze), or a "weathered wood" type gray that is compatible with your roof - also agree that charcoal would work. Personally, I am more of a fan of bringing a color, whether blue, green, or something else, Be sure to bring swatches, and then samples, to be sure your color is one that works well with the brick and roof. I would say paint the shutters, pillars, and the siding over the portico with the darker, more neutral color, then give the front door (and all of the trim around it) a more "pop" color - which doesn't have to be anything terrible different , perhaps just a few shades lighter/more stand out than the new trim color. (Example, if you chose Urbane Bronze, you could do your door in a compatible, slightly grayish blue). I would encourage you to paint the garage doors in a tone that blends them into the brick more - you want your entry area to be the eyecatcher, not the garage! I know that it is a "rule" that shutters should be sized to look functional, but I don't always agree - in our contemporary architecture, when the window usually lacks attractive framing (like brick mold, for example) and you don't want them to disappear visually, or you need to balance another element (like huge garage doors) shutters can do that - like jewelry. I think that is the case here, and I would not remove them. If you did decide to remove, then paint the window frames in a darker color . I would like to see those painted keystones unpainted or repainted to blend in with the brick also..