It has been reported that some centralised exchanges will deny deposits of cryptocurrency that come from tumblers/mixers, for reasons perhaps related to ownership of the coins. If one was concerned with these or other such issues, are there any services that allow one to examine the bitcoin prior to purchase, so that one can check if they have been through a tumbler/mixer or other dubious source prior to purchase?
I don't think such a service exists for a few reasons, like that it would be impractical.
When you buy on a centralized exchange, you're not actually buying a specific coin (UTXO) but rather a promise that you can withdraw the specified amount. Since the pool of coins that users withdraw from (the exchange's hot wallet) is constantly changing, you can't know which coin will be sent to you before you initiate the withdrawal. And since exchanges batch withdrawals for multiple users into one transaction, it's even less practical to ask each of them if they are fine with the coin they're receiving.
Regarding the question of ownership of stolen coins, that's really only applicable if your withdrawal is being funded from a UTXO that comes directly from a deposit of the stolen bitcoin. If the exchange previously combined that coin with other "clean" coins into one large UTXO (example transaction), then no one specifically can be pinpointed as having received the stolen bitcoin. You can reach out to your exchange and ask the specifics of their coin management.