Atlas had traditionally been a place that has had its own distinct character and political tilt, but also one with healthy amounts of posters with minority views. These posters with minority views are crucial to seeing this place as interesting as it is, and filling a niche as a place where people of wildly different positions can debate. So no, Woody should not be banned for his views, no matter how reprehensible, if his behavior does not violate the TOS.
After all, Netanyahu is a genocidal maniac who has killed more children in Gaza than Putin in Ukraine, yet no one has brought up banning Netanyahu supporters.
This is an explicit blood libel reliant on the fact that 90% of the deaths in Ukraine are off-books in Russian-controlled cities that have been essentially liquidated.