diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index f047fe1809aa..97c432f13fa8 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -1274,9 +1274,10 @@ def sharex(self, other):
         self._sharex = other
         self.xaxis.major = other.xaxis.major  # Ticker instances holding
         self.xaxis.minor = other.xaxis.minor  # locator and formatter.
+        # Set scale before limits to avoid warnings with non-linear scales
+        self.xaxis._scale = other.xaxis._scale
         x0, x1 = other.get_xlim()
         self.set_xlim(x0, x1, emit=False, auto=other.get_autoscalex_on())
-        self.xaxis._scale = other.xaxis._scale
 
     def sharey(self, other):
         """
@@ -1293,9 +1294,10 @@ def sharey(self, other):
         self._sharey = other
         self.yaxis.major = other.yaxis.major  # Ticker instances holding
         self.yaxis.minor = other.yaxis.minor  # locator and formatter.
+        # Set scale before limits to avoid warnings with non-linear scales
+        self.yaxis._scale = other.yaxis._scale
         y0, y1 = other.get_ylim()
         self.set_ylim(y0, y1, emit=False, auto=other.get_autoscaley_on())
-        self.yaxis._scale = other.yaxis._scale
 
     def __clear(self):
         """Clear the Axes."""
@@ -1419,6 +1421,9 @@ def __clear(self):
             share = getattr(self, f"_share{name}")
             if share is not None:
                 getattr(self, f"share{name}")(share)
+                # Don't set default limits for shared axes - they will be
+                # synchronized from the shared axis and may have non-linear
+                # scales that would reject the (0, 1) default limits.
             else:
                 # Although the scale was set to linear as part of clear,
                 # polar requires that _set_scale is called again
diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index c3b6fcac569f..bf0bbcdf3b21 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1263,7 +1263,14 @@ def _set_lim(self, v0, v1, *, emit=True, auto):
             for other in self._get_shared_axes():
                 if other is self.axes:
                     continue
-                other._axis_map[name]._set_lim(v0, v1, emit=False, auto=auto)
+                # Skip propagating default (0, 1) limits from linear scale to
+                # non-linear scales during clear operations to avoid warnings
+                other_axis = other._axis_map[name]
+                if (self.get_scale() == 'linear' and
+                    other_axis.get_scale() != 'linear' and
+                    v0 == 0 and v1 == 1):
+                    continue
+                other_axis._set_lim(v0, v1, emit=False, auto=auto)
                 if emit:
                     other.callbacks.process(f"{name}lim_changed", other)
                 if ((other_fig := other.get_figure(root=False)) !=