我认为您可以to_datetime使用参数解析，errors='coerce'然后将strftime其转换为工作日作为语言环境的全名：
print df
TRX_DATE some value
0 2010-08-15 13:00:00 27.065
1 2010-08-16 13:10:00 25.610
2 2010-08-17 02:30:00 17.000
3 2010-06-18 02:40:00 17.015
4 2010-18-19 02:50:00 16.910
df['TRX_DATE'] = pd.to_datetime(df['TRX_DATE'],errors='coerce')
df['day_type'] = df['TRX_DATE'].dt.strftime('%A')
print df
TRX_DATE some value day_type
0 2010-08-15 13:00:00 27.065 Sunday
1 2010-08-16 13:10:00 25.610 Monday
2 2010-08-17 02:30:00 17.000 Tuesday
3 2010-06-18 02:40:00 17.015 Friday
4 NaT 16.910 NaT
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