Some Baptists do, but others do not. One of my closest friends is a Southern Baptist pastor whose leader teaches that there is a demon also named “Jesus” who is the God of false churches (including, in his view, both Catholics and Mormons). I disagree, and believe Jesus heeds the cry of those who call out to him as Savior, whatever conception of theology they may have (if it is genuine,even if it be in ignorance or error).
I have to agree with you!