Does a wooden ruler block magnetism?

No. Wood does not have any magnetic response at DC (i.e., at low frequencies like when using a bar magnet or a refrigerator magnet to move around metal shavings). Of course if the ruler is too thick then the shavings will be too far away from the magnet and nothing will happen, but then it is not the wood's fault, it is only because of the distance between the magnet and the metal shavings.