SAS date valued variables are numeric and should have a format such as MMDDYY10. assigned.
If your date variable is an actual SAS date value the code should be
if Date >= '01OCT2019'd
then Variable= "X";
Literal dates must be in the date9 or date7(not recommended) 01OCT2019 format, in quotes and with the D to tell SAS that the value is intended to be a date.
In some locals 10/01/2019 would be 10 January 2019 and if you do something like 01/02/03 it is impossible to tell which might actually be the year. So SAS uses the 'ddmmmyyyy'd as a way to know which specific date is intended.
What your code is actually doing is telling SAS to divide 10 by 1, then divide that result by 2019.
You could test that with code like:
data junk;
date='01JUN2018'd;
z = 10/01/2019;
if Date >= z then Variable= "X";
if date >='01OCT2019'd then var2 = 'X';
run;
A value of Z in that range will be considered to be 01Jan1960.
https://communities.sas.com/t5/SAS-Communities-Library/Working-with-Dates-and-Times-in-SAS-Tutorial/... has a PDF with much information about dates.