So you have no problem with Christians exercising what they believe to be their 'great commission' to spread the gospel throughout the Earth? Christians also believe that you cannot force Christianity onto anybody, but is a process of attracting people to know the One who is the right path so that they choose it themselves.
I'm not familiar enough with the Sunnah to answer that question authoritatively. I doubt there would be an issue with proselytization by non-Muslims among non-Muslims, but I'm not sure about attempting to convert Muslims to other faiths. Historically, this has been forbidden. I don't know whether it should be or not, so I'll try to do some research.
I am unaware of any predominantly Christian countries in which it is illegal for Muslims to actively advertise and promote their faith and encourage (proselytize) anybody, including Christians, to join them.
I am unaware of any predomantly Muslim country in which it is legal for Christians to actively advertise and promote their faith and encourage (proselytize) anybody, much less Muslims, to join them.