Checking non-dimensional coordinates for equality

Code Sample, a copy-pastable example if possible

I'm working on a proof-of-concept for the geoxarray project where I'd like to store coordinate reference system (CRS) information in the coordinates of a DataArray or Dataset object. I'd like to avoid subclassing objects and instead depend completely on xarray accessors to implement any utilities I need.

I'm having trouble deciding what the best place is for this CRS information so that it benefits the user; .coords made the most sense. My hope was that adding two DataArrays together with two different crs coordinates would cause an error, but found out that since crs is not a dimension it doesn't get treated the same way; even when changing join method to 'exact'.

from pyproj import CRS
import xarray as xr
import dask.array as da

crs1 = CRS.from_string('+proj=lcc +datum=WGS84 +lon_0=-95 +lat_0=25 +lat_1=25')
crs2 = CRS.from_string('+proj=lcc +datum=WGS84 +lon_0=-95 +lat_0=35 +lat_1=35')


a = xr.DataArray(da.zeros((5, 5), chunks=2), dims=('y', 'x'), coords={'y': da.arange(1, 6, chunks=3), 'x': da.arange(2, 7, chunks=3), 'crs': crs1, 'test': 1, 'test2': 2})      

b = xr.DataArray(da.zeros((5, 5), chunks=2), dims=('y', 'x'), coords={'y': da.arange(1, 6, chunks=3), 'x': da.arange(2, 7, chunks=3), 'crs': crs2, 'test': 2, 'test2': 2})            

a + b                                                                                                                                                                              
# Results in:
# <xarray.DataArray 'zeros-e5723e7f9121b7ac546f61c19dabe786' (y: 5, x: 5)>
# dask.array<shape=(5, 5), dtype=float64, chunksize=(2, 2)>
# Coordinates:
#   * y        (y) int64 1 2 3 4 5
#   * x        (x) int64 2 3 4 5 6
#     test2    int64 2

In the above code I was hoping that because the crs coordinates are different (lat_0 and lat_1 are different and crs1 != crs2) that I could get it to raise an exception.

Any ideas for how I might be able to accomplish something like this? I'm not an expert on xarray/pandas indexes, but could this be another possible solution?

Edit: xr.merge with compat='no_conflicts' does detect this difference.

Start by reproducing the DataArray addition example with the two differing CRS coordinates, then inspect xarray's coordinate alignment and pandas index behavior. Compare this with xr.merge using compat='no_conflicts' and determine what a consistent equality check for non-dimensional coordinates would need to guarantee.