Turns out, Tableau had problems interpreting posted dates. I changed date format in Tableau project, and it solved the issue.
Originally, the filter was set to "Month" format, which Tableau displays as "[Month] [Year]" - so it should have been fine, but apparently it could not parse date string correctly. I changed it to "MMMM YYYY" - it solved the issue.
I'm still confused as to why Tableau would sometimes work and be able to parse date string that's in the same format as the one it's being displayed in when set to "Month" format, though.