How about no? If it's my app, I'll use my logo. I consider the logo an integral part of the application's identity and I should control its identity. I promise I'll do my best to make it easily and readily recognizable, regardless of it using national colors, a rainbow or shades of white, pink and blue. If you don't like it, it's your problem, not mine.
You might own the app's code but if the user paid for the app, they're entitled to not wanting their screen to become some billboard to The Current Thing™. Buy a few billboards and airtime if you feel you should shove your political beliefs and opinions down everyone's throat. With this behavior, you're the representation of everything wrong with corporate political activism and the tech industry at large: You're the app's developer, and for some reason you think you know more than the user.