Is it legitimate to shun disbelievers, whether settlers or those coming to Islamic lands, and does this permit killing or robbing them if one observes them committing an abomination?

It is not permissible to kill a non-Muslim resident, or a visiting non-Muslim who has been granted safe passage by the state, nor is it permissible to kill disobedient individuals or transgress against them. Rather, their wrongdoings should be referred for a Shariah ruling.