BUG: replacing a string with None causes an unexpected forward fill 
- [X] I have checked that this issue has not already been reported.

- [X] I have confirmed this bug exists on the latest version of pandas.

- [ ] (optional) I have confirmed this bug exists on the master branch of pandas.

---

**Note**: Please read [this guide](https://matthewrocklin.com/blog/work/2018/02/28/minimal-bug-reports) detailing how to provide the necessary information for us to reproduce your bug.

#### Code Sample, a copy-pastable example

```python
# Your code here
df = pd.DataFrame(np.zeros((3, 3)))
df.iloc[2, 2] = ''
df = df.replace('', None)
print(df.iloc[2, 2] == '') # prints False
print(df.iloc[2, 2] == df.iloc[1, 2]) # prints True

```

#### Problem description

[this should explain **why** the current behaviour is a problem and why the expected output is a better solution]

#### Expected Output
Replacing a string with a None should introduce a None, not forward fill the previous result. 

#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : db08276bc116c438d3fdee492026f8223584c477
python           : 3.6.5.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 19.6.0
Version          : Darwin Kernel Version 19.6.0: Thu Jun 18 20:49:00 PDT 2020; root:xnu-6153.141.1~1/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.1.3
numpy            : 1.19.2
pytz             : 2018.9
dateutil         : 2.8.1
pip              : 20.2
setuptools       : 49.2.0
Cython           : None
pytest           : 5.4.3
hypothesis       : None
sphinx           : 1.8.3
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : 4.5.1
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.10.1
IPython          : 7.13.0
pandas_datareader: None
bs4              : 4.9.0
bottleneck       : None
fsspec           : None
fastparquet      : None
gcsfs            : None
matplotlib       : 3.2.2
numexpr          : None
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : None
pytables         : None
pyxlsb           : None
s3fs             : None
scipy            : 1.4.1
sqlalchemy       : 1.3.16
tables           : None
tabulate         : None
xarray           : None
xlrd             : None
xlwt             : None
numba            : None

</details>
