I don't exactly recieve a weekly allowance with money, per se, but at the end of every week my mom takes me to the city for shopping. This is how I obtain most of my manga.
One day, we were in line, and I had two volumes that I wanted to purchase. My mom took them from me, and at times she looks at the volumes while standing in line. Not really flipping through them, but sometimes she reads the back cover. Now, my mom had never had any problems with buying me manga based on ratings. They could be T+, or M, she wouldn't have a problem with it. But that day, she happened to notice the Explicit Content label on the cover of one volume, and asked me to put it back. In the end, I did get it because I basically began explaining to her about the volume in line, and how the content wasn't really THAT explicit. XP
A few times, my mom has sworn to stop buying me manga because she doesn't consider them "books," but I found that this is a vague threat and never happens.
She has also given me a few speeches on the mature nature of manga, and how she worries it affects me. XD But this is probably common.
Anyways, what do your parents think of manga?