This also only works if both the violent and non-violent groups have matching demands. In a case where the violent group has demands that pertain specifically or mostly to their own group, then they can be separately appeased by those in power which leaves the non-violent group without any leverage and they can thus be cracked down on.

This is what happened to a lot of Native American tribes in the past 200 years. Given two different tribes in the same geographical region, one violent and the other non-violent, the violent tribe got some concessions like official reservation land in a better area in exchange for peace, while the non-violent tribe often got nothing except brutal genocide. This is more true in the American Midwest and West coast—the Eastern tribes often got nothing at all for either approach.