It depends on your industry, brand and context.
Generally speaking, you’ll want to use a backdrop that emphasizes your brand identity.
Working in financial services or law?
Go for a dark or mid-tone gray backdrop.
Getting employee headshots for your tech startup?
Go with a fun-colored backdrop or outdoors.
For geographically dispersed teams with locations in multiple cities, you should probably consider using a commonly available backdrop color. That way, you can source similar headshots from a variety of photographers across teams.
Perfect consistency across all employee photos isn’t an absolute necessity, but there’s something special about a website “About Us” page with precisely consistent headshots for the whole executive team, executive board, or even entire staff.