That problem is very easy to deal with. Use a public printer and pay with cash or buy a used printer with cash and use it somewhere away from your house. Or cut a stencil from cardboard and make them yourself with gloves using a permanent marker, or just write the posters yourself with blocky letters that don't resemble your handwriting.

Of course that's not necessary because of the forensic effort it would take to track your posters. But if you want to be extra careful it's not hard.