As far as I know, there is no way to tell Google Sheets the types of individual values. That is, you can either tell Google Sheets to infer type based on what the data looks like or send it raw. Could you please confirm, @Grzesiek2010?
Initially the type was inferred by Google Sheets but this caused data loss in certain cases, especially with select multiples (see Strange output from "select_multiple" questions).
The apostrophe is a special character recognized by most spreadsheet programs including Google Sheets as indicating that the value is raw. It should still be possible to do calculations with those values.
I tried putting '09/10/2019 in cell A1 and was able to confirm that =weekday(A1) in another cell works as intended.
What calculation is failing?