Passing datetime-like object to seaborn.lmplot

You need to convert your dates to floats, then format the x-axis to reinterpret and format the floats into dates.

Here's how I would do this:

import pandas
import seaborn
from matplotlib import pyplot, dates
%matplotlib inline

date = ['1975-12-03','2008-08-20', '2011-03-16']
value = [1,4,5]
df = pandas.DataFrame({
    'date': pandas.to_datetime(date),   # pandas dates
    'datenum': dates.datestr2num(date), # maptlotlib dates
    'value': value
})

@pyplot.FuncFormatter
def fake_dates(x, pos):
    """ Custom formater to turn floats into e.g., 2016-05-08"""
    return dates.num2date(x).strftime('%Y-%m-%d')

fig, ax = pyplot.subplots()
# just use regplot if you don't need a FacetGrid
seaborn.regplot('datenum', 'value', data=df, ax=ax)

# here's the magic:
ax.xaxis.set_major_formatter(fake_dates)

# legible labels
ax.tick_params(labelrotation=45)