Concerning the F.O.P. there are three "lodges" that will solicit you for donations. The national lodge, the state lodge and the local lodge.
The national as well as the state lodges are soliciting for donations simply for their administration and political lobbying.
The local lodges solicit funds for their own administration (building upkeep, etc...) but they also do it for local charity programs (such as "Shop with a Cop, etc...) and other events that they run throughout the year.
When solicitied for a donation, ask whether it is being requested for the National, State or local lodge. Out of the three, a donation to the local lodge is the only one that will benefit locally.
As for the stickers...they are given out to anyone and don't really mean much. I give warnings to people because of their manners and attitude, not because they have a sticker.