Yeah I share your pain @dreycenfoiles , I also work with Multiindex all the time 
I have a workflow similar to yours that I tend to use, but very recently I ended throwing that away and doing something much simple. Just use something like:
"obs_id": [
f"{date}_{loc}_{state}" for date, state, loc in Y[["date", "loc", "state"]].to_numpy()
]
Then, you can index your InferenceData object with isel, using your Y dataframe with the specific combinations of date and location (for instance) that you want:
idata.isel(obs_id=Y[select_with_pandas].index)
So yeah, I’m basically outsourcing the selection to Pandas
But the fact that xarray can’t handle selection on Multiindex (at least that I know of) is a huge limitation for me in these cases.
Another advantage of this solution is that it avoids unstack or reset_index("obs_id") which are both computationally intensive – if you have big data, your RAM will break down
Hope this helps 