I agree with everyone here, with one caveat: There is a reason that the TOR browser exists. It masks your traffic by throwing it out a bunch of different endpoints at random.
The use case that this user is describing specifically (their users looking up their public IP and sharing it with a threat actor) would not be prevented by changing or masking the public IP, but if they have a specific need to prevent the traffic they are shipping from being associated with a specific IP, that would be a different conversation.
@Prince - Your users will always be able to see their public IP through some means, no matter what content filtering or masking you put in place.