Contrary to one post here, “total depravity” does not necessarily include being born guilty of Adam’s sin. Surely Ulrich Zwingli (the real father of the Reformed tradition) did not deny total depravity, but he did deny that children are born guilty of Adam’s sin. Most Reformed Baptists deny it as well while still holding to total depravity.
All that is required for belief in total depravity is belief that all persons (except Jesus Christ) since Adam are born with a corruption of nature such that willful sinning and consequent guilt are inevitable and that every aspect of a human person’s nature is corrupted by sin. Most free church evangelicals and Baptists have always held this view of original sin and total depravity–whether they are Calvinists or Arminians.
If a person is going to declare everyone who does not believe in inherited guilt “not orthodox,” that would include a whole lot of Calvinists including many (I would say most) Reformed Baptists, Calvinist Evangelical Free members, etc.