BUG: Index.get_indexer casts values is given as list

[phofl]

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Reproducible Example

pd.options.future.infer_string = True

idx = pd.Index(["a", "b", None], dtype="object")
idx.get_indexer([None, "x"])


[-1 -1]

Issue Description

We cast the iterable to an Index, which will cast None to NaN and thus the fixtures won't match anymore. I think it makes sense here to keep object if idx is also object dtype?

cc @jbrockmendel @jorisvandenbossche

Expected Behavior

See above

Installed Versions

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[jorisvandenbossche]

I would expect we coerce the list to an Index with the dtype of the calling index, but so that is not the case?

At least for object dtype we should do that, I think. Also without the string inference, you can already run into "issues" with this in case of mixed objects:

In [34]: idx = pd.Index(["a", 0.2, None], dtype="object")

In [35]: idx.get_indexer([0.2, None])
Out[35]: array([ 1, -1])

[phofl]

No we do the inference without taking the dtype of self into account

[jbrockmendel]

I think it makes sense here to keep object if idx is also object dtype?

In most cases in get_indexer we end up casting self/target to a common dtype, which would be object in this case anyway. So avoiding the inference step wouldn't be so bad. The caveats that come to mind are 1) _maybe_downcast_for_indexing can downcast in some cases, 2) i think Categorical has some special handling, 3) in a perfect world we'd avoid that upcasting altogether