In most cases, no. However, some people consider it polite to ask your neighbors’ opinion before painting any part of your home’s exterior a bright or “outlandish” color.
If you live somewhere with curb appeal guidelines, such as in an area with a homeowners’ association (HOA), then there might be rules about which colors you can paint your front door. These guidelines will vary greatly, so check with your HOA before changing your front door color.