LDS, those are Fast Offering
collections. Not many wards (congregations) at all use this anymore.
When it is done, the young man offers the envelope to the person, who then can easily walk away, into another room, and put money into the envelope, or not, as he sees fit. The very slight hint of coersion associated with this practice is the reason that it has died out. Even where it is still practiced, anyone at all can ask that they not receive these visits.
Now, as to the consequences of not paying tithes:
The main consequence is that the person cannot go to the Temple. This means that they cannot attend Temple weddings or participate in the special ordinances that occur there.
There are a very few "callings" or positions of authority that someone who doesn't pay their tithes will be blocked from.
Someone who doesn't pay their tithes will not be able to attend one of the four or five Church-owned schools (BYU, BYU-Idaho, BYU-Hawaii, or the LDS Business
College [did I miss any?]).
In order to go on a mission, the young adult must be paying a full tithe.
Those are the only consequences I can think of. A very secular example of this is this very forum. Some advantages are reserved for those who pay. However, those who don't pay, are given great advantages anyway. Participation is purely voluntary, as is payment.
The difference is that we believe that tithes are a commandment from God. The forum is just educational and fun.