align skips alignment checks for indexes that are not reindexed #10714

from xarray import align, Dataset
ds1 = Dataset(coords={"x": [1, 2, 3], "xb": ("x", [4, 5, 6])}).set_xindex("xb")
# Swap two values in only "xb" only
ds2 = Dataset(coords={"x": [1, 2, 3], "xb": ("x", [4, 6, 5])}).set_xindex("xb")
# Swap two (different) values in both coordinates
ds3 = Dataset(coords={"x": [2, 1, 3], "xb": ("x", [4, 6, 5])}).set_xindex("xb")

align(ds1, ds2)  # --> no error       (which is wrong)
align(ds1, ds3)  # --> AlignmentError (as expected)

# Source: xarray/structure/alignment.py

    def _get_dim_pos_indexers(
        self,
        matching_indexes: dict[MatchingIndexKey, Index],
    ) -> dict[Hashable, Any]:
        dim_pos_indexers: dict[Hashable, Any] = {}
        dim_index: dict[Hashable, Index] = {}

        for key, aligned_idx in self.aligned_indexes.items():
            obj_idx = matching_indexes.get(key)
            if obj_idx is not None and self.reindex[key]:
                #######################################################################
                # ↓ None of this code is run for indexes that require no reindexing ↓ #
                #######################################################################
                indexers = obj_idx.reindex_like(aligned_idx, **self.reindex_kwargs)
                for dim, idxer in indexers.items():
                    if dim in self.exclude_dims:
                        raise AlignmentError(
                            f"cannot reindex or align along dimension {dim!r} because "
                            "it is explicitly excluded from alignment. This is likely caused by "
                            "wrong results returned by the `reindex_like` method of this index:\n"
                            f"{obj_idx!r}"
                        )
                    if dim in dim_pos_indexers and not np.array_equal(
                        idxer, dim_pos_indexers[dim]
                    ):
                        raise AlignmentError(
                            f"cannot reindex or align along dimension {dim!r} because "
                            "of conflicting re-indexers returned by multiple indexes\n"
                            f"first index: {obj_idx!r}\nsecond index: {dim_index[dim]!r}\n"
                        )
                    dim_pos_indexers[dim] = idxer
                    dim_index[dim] = obj_idx

        return dim_pos_indexers