If I see a neighbors inappropriate mail, am I allowed to throw it out?
I think there are a few different scenarios here:
- Shmerel looks into his neighbor Berel's mailbox, and sees something inappropriate.
Mind your own business. Messing with his mailbox is a federal crime. Dina d'malchusa dina.
R' Moshe Feinstein once dealt with a fellow who would seize people's (totally appropriate) stuff and demand they give tzedaka before he'd give it back. The question was whether the guy was sane.
- Due to a postal error, Shmerel receives a piece of inappropriate mail, addressed to his neighbor Berel.
That's a tougher question; are you actively facilitating a sin by now delivering it to Berel? My gut reaction is neither to throw it out, nor to deliver it yourself. Mark it "WRONG ADDRESSEE" and let the post office figure it out.
There may certainly be cases where it's advisable or even required to offer constructive criticism to Berel, but that's a complicated topic, and may depend on how Berel will receive the criticism.
- A yeshiva has a policy of screening all incoming student mail
This one has been addressed in the literature. I know Rabbi Frand has a tape on the subject. If you enter the yeshiva on its terms, and the halachic prohibition on reading others' mail (formalized by Rabbeinu Gershom) is intended for the individual's wellbeing, but in this case the yeshiva is certain that he's better off not receiving this mailing, that's a different story.