Object dtype gives ValueError in _maybe_cast_with_dtype 
#### 

```python
import pandas as pd
import numpy as np

frame = pd.DataFrame(index=pd.Index([1, np.nan]))
fixed_index = frame.index.where(frame.index.notna(), 'a' + frame.reset_index().index.astype(str))

Traceback (most recent call last):
  File "<input>", line 4, in <module>
  File "C:\Users\Miniconda3\envs\testbed_dtype\lib\site-packages\pandas\core\indexes\base.py", line 3791, in where
    return self._shallow_copy_with_infer(values, dtype=dtype)
  File "C:\Users\Miniconda3\envs\testbed_dtype\lib\site-packages\pandas\core\indexes\base.py", line 567, in _shallow_copy_with_infer
    return Index(values, **attributes)
  File "C:\Users\Miniconda3\envs\testbed_dtype\lib\site-packages\pandas\core\indexes\base.py", line 385, in __new__
    data = _maybe_cast_with_dtype(data, dtype, copy)
  File "C:\Users\Miniconda3\envs\testbed_dtype\lib\site-packages\pandas\core\indexes\base.py", line 5457, in _maybe_cast_with_dtype
    data = data.astype(dtype)
ValueError: could not convert string to float: 'a1'
```
#### Problem description

Data is being cast to incorrect dtype based on inferred dtype and gives a ValueError.
Issue was not present in pandas==0.25.3

#### Expected Output
With pandas==0.25.3

fixed_index
Index([1.0, 'a1'], dtype='object')

#### Output of ``pd.show_versions()``
python           : 3.7.6.final.0
pandas           : 1.0.1
numpy            : 1.18.1
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 20.0.2
setuptools       : 45.2.0.post20200210
Cython           : None
pytest           : None
hypothesis       : None
sphinx           : None
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : None
IPython          : None
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : None
matplotlib       : None
numexpr          : None
odfpy            : None
openpyxl         : 3.0.3
pandas_gbq       : None
pyarrow          : None
pytables         : None
pytest           : None
pyxlsb           : None
s3fs             : None
scipy            : None
sqlalchemy       : None
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : 1.3.0
xlsxwriter       : None
numba            : None

</details>
