deprecate should_ignore_error

CHANGES.rst

@@ -14,6 +14,8 @@ Unreleased
     If subclasses were overriding these methods, the old signature is detected,
     shows a deprecation warning, and will continue to work during the
     deprecation period. :issue:`5815`
+-   The ``should_ignore_error`` is deprecated. Handle errors as needed in
+    teardown handlers instead. :issue:`5816`
 -   ``template_filter``, ``template_test``, and ``template_global`` decorators
     can be used without parentheses. :issue:`5729`
 -   ``redirect`` returns a ``303`` status code by default instead of ``302``.