I was a finance clerk for a year or so.
A person could put money in an envelope and mail it to the bishop. I have not been a bishop so I could not tell you how this money is processed. I do know that not all of the donations are from members of The Church Of Jesus Christ Of Latter Day Saints.
Here in the United States, the church requires both online *and* physical records to be kept.
How it works is that a member of the bishopric and a second authorized person - usually the finance clerk - open each envelope individually. They note in the computer system who gave the donation, what they're donating to, and then manually inspect the enclosed amount to ensure that it matches up. For example, if a person said they put $50 in cash, there's a count to ensure that there's actually $50 in cash.
This is done for every single envelope received that day.
Once the total count is done, a final manual count is done to ensure that the amount of cash received matches what the system says it should be, and that all of the checks / money orders / et cetra sync up as well.
Once this is all done and everything is entered into the computer with appropriate digital signatures, a digital notice is sent back to Salt Lake. The computer then spits out an assortment of documents, some of which need physical signatures. Specific documents, the white tithing slips, and certain other documentation are then placed in an envelope and placed inside a designated filing cabinet. These documents are audited every six months, and IIRC anything & everything may be audited as far out as two years from date.
On the physical end, the money and payments are placed in a bank deposit envelope along with copies of certain record documents, both ones printed by the system and created by an NCR paper ledger. The two people who prepared everything must then take the sealed envelope to the designated drop point, which 9 times out of 10 will be the night drop box at a specific local bank that the church has set up an account with. For purposes of operational security, I won't explain the rare instance on open comms.
how would anonymous tithing be done?
if they are paying tithes online, that would probably be done with a credit card so it couldn't be anonymous.
if the church's website will accept Bitcoin or other cryptocurrency, that would have the potential for anonymous giving.
is that kind of system in place?
can an LDS simply put cash into the donation box outside of the Bishop's office when no one is around?
There isn't a cash donation box. There's supposed to be a record kept of everything.
Story time -> When I was the finance clerk, news broke that the State of California Democratic Party had been robbed blind by their top finance official. The party's internal financial security standards were so weak that she was able to pilfer millions of dollars from them, and the only reason they caught it was because checks started bouncing. The audit standards I had to abide by as a branch finance clerk were stricter than an entire state-level political party was operating under.
A person does not have to pay a full tithe to go to tithing settlement. They can declare that it is not a full tithe. Members do not need to have a temple recommend to be members. I know one person that attended church with his wife for many years before becoming a member. I paid tithing for many years before I got a temple recommend.
If a person has specific circumstances, circumstances to which I was not personally privy, then they can be designated as "exempt". I wouldn't know who was or wasn't until at the end of each year when I was tasked with officially registering in the system who declared themselves to be a full or partial tithe-payer.
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