You will likely lose those donations if audited, there is not much way around it. The alternative is not to put loose cash into a counter-top cash box at Mcdonalds, for example, but to mail a check to the RM house or make an electronic donation online.
For all donations you are required to have a bank record. This can be a credit card statement or canceled check. The recipient is only required to issue a receipt if the donation is more than $250, or more than $75 if the transaction is partly a donation and partly for a service. (Like tickets to a charity dinner where you have to account for the value of the dinner).
The receipt has to be from the recipient organization. That would normally require an authorized person. That doesn't have to be a high official -- the kid at the back door of Goodwill issues receipts when you bring in your old household stuff, so is probably authorized. But I doubt that counter employees of one company who have custody of a cash box or donation bucket for a third party organization would be authorized to issue a receipt if you asked, and I doubt it would be accepted as valid. (The kid at McDonalds is not a representative of RM House and probably can't issue a legal receipt in their name.)
If this is a problem you can simply change your pattern of donation, make online gifts with electronic records instead of cash gifts into anonymous cash boxes.
Also, since the standard deduction is doubled with tax reform, many fewer taxpayers will have enough deductions to be worth itemizing.
