Is it permissible to buy and eat meat and poultry sold by a non-Muslim butcher who claims it is halal, when there are Muslim butchers selling halal meat in the same area?

It is preferable to buy meat from Muslims to support them and renew the bond of faith. If that is not possible, then the slaughtered animal of the People of the Book (Jews and Christians) is permissible by scholarly consensus, based on the Almighty's saying: (The food of those who were given the Scripture is lawful for you) [Al-Ma'idah/5]. There is no need to inquire about the method of slaughter, because the presumption is that their slaughter is valid, unless one ascertains that the slaughter is unlawful.