Adding non-dimension string coordinate gives different interpolation results

What happened?

When I interpolate on data by taking a mean along the y dimension the presence of a non-dimension string coordinate makes a difference to the result. I would expect this non-dimension coordinate to be passive.

What did you expect to happen?

I would expect the results to be independent of the non-dimension coordinate string_coord being present or not. But when string_coord is present I get:

<xarray.DataArray (x: 2, y: 2)>
array([[0. , 0.1],
       [0. , 0.1]])
Coordinates:
  * x             (x) int64 0 1
  * y             (x) float64 0.05 0.05
    string_coord  (x) <U21 '0' '1'

whereas after I uncomment the line where I add the non-dimension string coordinate I get the expected result:

<xarray.DataArray (x: 2)>
array([0.005, 0.005])
Coordinates:
    y        (x) float64 0.05 0.05
  * x        (x) int64 0 1

Minimal Complete Verifiable Example

import xarray as xr
import numpy as np
data = np.array([[0.0 , 0.1 ],
    [0.0, 0.1]])
data = xr.DataArray(
    data,
    coords=dict(
        x=[0,1],
        y=[0,1]
        )
)
data["string_coord"] = data.x.astype("str")
data_mean = data.mean(dim="y")
interp_data = data.interp(y=data_mean, method="linear")
print(interp_data)

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Relevant log output

No response

Anything else we need to know?

No response

Environment

Start by running the minimal Python example against the current xarray checkout and compare interpolation with and without string_coord. Trace the interpolation path used by DataArray.interp after mean(dim="y"). Done means the non-dimension string coordinate no longer changes the interpolation result, with a regression test covering the example.