Stuck trying to remove default date

What I am trying to say is that I find it strange that khorseman's suggestion isn't working for you, since it does work for me.

Could be your Power BI desktop version, or may be something with the column type.

Here is what I did.

1. Create a sample table with two columns. A text and a date column.
2. Fill the table witj some dummy data, including one date with 1-1-1900
3. Use Khorseman's suggestion of the value replacer, I can insertt null without issue (see screenshot 1)
   
4. Result after the action can be seen in screenshot 2
   
   

   = Table.ReplaceValue(#"Changed Type",#date(1900, 1, 1),null,Replacer.ReplaceValue,{"Column2"})

5. Since that isn't working for you, you might want to try this work around. (step 6 and beyond)
6. Replace 1-1-1900 with 1-1-1901
   
   

   = Table.ReplaceValue(#"Changed Type",#date(1900, 1, 1),#date(1901, 1, 1),Replacer.ReplaceValue,{"Column2"})

7. See what code is generated.
8. Try to swap that code, with the code that is genarated for a null value

Good luck

p.s. an alternative would be to edit the SQL statement according to your needs with a CASE statement, you could also try something like

CASE date='1-1-1900' THAN null ESLE date END AS date

Could be a little different based on your datasource, but you can google the specifics of a case statement for your database.