From eBay's FAQ about the new payment policies:
Quote
What should I do if I have long-standing, repeat customers who insist on paying with checks or money orders, even after I explain the benefits of electronic payments and offer suggestions?
We know this may happen occasionally, and if you accept checks or money orders from these customers a reasonably small percentage of the time, this will not be a violation of the new payments policy. However, we will not allow abuse of the new policy and will be watching for sellers who accept a significant amount of prohibited payments. Remember also, you can refuse to accept these payment methods. If the buyer doesn't pay, you can file an unpaid item (UPI) complaint. Buyers who insist on paying with these prohibited payment methods in a UPI claim will lose the claim and will not be allowed to leave negative feedback.
http://pages.ebay.com/sell/August2008Update/OtherFAQ/index.html#3
AND
* eBay will not automatically take action against a seller with a low completion rate. We realize that there are many valid reasons for low completion rates, including the one raised by @Amber, who posted that she frequently uses PayPal invoices with her buyers. (We are reviewing the checkout flow with an eye towards determining and eliminating the most common reasons a seller is forced to resort to PayPal invoicing for eBay sales.)
* We will investigate sellers with low checkout completion rates on a case by case basis. Specifically, we will check to see if the seller is soliciting check or money order payment from their buyers. If we don’t find any evidence of this occurring, we won’t take action against the seller.
It appears like it'll be business as usual for the sellers who accept mailed payments but get them rarely. What the "signifcant amount" could be any number though.
* eBay will not automatically take action against a seller with a low completion rate. We realize that there are many valid reasons for low completion rates, including the one raised by @Amber, who posted that she frequently uses PayPal invoices with her buyers. (We are reviewing the checkout flow with an eye towards determining and eliminating the most common reasons a seller is forced to resort to PayPal invoicing for eBay sales.)
My take and other boards understanding is this: You won't be able to advertise that you accept payments other than PP, however if a buyer uses ask a question to ask if you accept checks/money orders, you can say yes.