Does Primer need to be filtered
Absolutely this! Those strainers don't cost jack squat up front but can save you hours or hundreds of dollars in the end.
Clog a gun on primer and it's extra sanding. What you just spent on the extra abrasives cost way more than that strainer.
Clog a gun on your sealer, causing an uneven pattern and a run... Now you are wiping off and redoing some of your sealer. This cost way more than that strainer.
And it only gets worse from here.