diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index 7424c4ddc3d92..979dad6db0838 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -1,4 +1,5 @@
 from datetime import datetime, timedelta, date
+import warnings
 
 import cython
 
diff --git a/pandas/_libs/index_class_helper.pxi.in b/pandas/_libs/index_class_helper.pxi.in
index 3c9a096e7ecc0..4db048eeb0383 100644
--- a/pandas/_libs/index_class_helper.pxi.in
+++ b/pandas/_libs/index_class_helper.pxi.in
@@ -60,7 +60,16 @@ cdef class {{name}}Engine(IndexEngine):
 
         # A view is needed for some subclasses, such as PeriodEngine:
         values = self._get_index_values().view('{{dtype}}')
-        indexer = values == val
+        try:
+            with warnings.catch_warnings():
+                # e.g. if values is float64 and `val` is a str, suppress warning
+                warnings.filterwarnings("ignore", category=FutureWarning)
+                indexer = values == val
+        except TypeError:
+            # if the equality above returns a bool, cython will raise TypeError
+            #  when trying to cast it to ndarray
+            raise KeyError(val)
+
         found = np.where(indexer)[0]
         count = len(found)
 
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index 6c95b521110a9..c0436e9389078 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -349,7 +349,7 @@ def _decide_output_index(self, output, labels):
             output_keys = sorted(output)
             try:
                 output_keys.sort()
-            except Exception:  # pragma: no cover
+            except TypeError:
                 pass
 
             if isinstance(labels, MultiIndex):
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 6deef16bdec13..55def024cb1d4 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -727,8 +727,7 @@ def f(g):
         with option_context("mode.chained_assignment", None):
             try:
                 result = self._python_apply_general(f)
-            except Exception:
-
+            except TypeError:
                 # gh-20949
                 # try again, with .apply acting as a filtering
                 # operation, by excluding the grouping column
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index 31623171e9e63..d079a1c4ef4f7 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -592,9 +592,11 @@ def is_in_axis(key):
 
     # if the grouper is obj[name]
     def is_in_obj(gpr):
+        if not hasattr(gpr, "name"):
+            return False
         try:
-            return id(gpr) == id(obj[gpr.name])
-        except Exception:
+            return gpr is obj[gpr.name]
+        except (KeyError, IndexError):
             return False
 
     for i, (gpr, level) in enumerate(zip(keys, levels)):
diff --git a/pandas/core/groupby/ops.py b/pandas/core/groupby/ops.py
index 7afb0a28f943e..6263973fb0d2f 100644
--- a/pandas/core/groupby/ops.py
+++ b/pandas/core/groupby/ops.py
@@ -212,8 +212,8 @@ def apply(self, f, data, axis=0):
                 # This Exception is also raised if `f` triggers an exception
                 # but it is preferable to raise the exception in Python.
                 pass
-            except Exception:
-                # raise this error to the caller
+            except TypeError:
+                # occurs if we have any EAs
                 pass
 
         for key, (i, group) in zip(group_keys, splitter):