Is it safe to rent to someone in an open chapter 13 bankruptcy?

What do you mean by "safe"? The rental agreement or lease will not be affected by the Chapter 13, but you as a prospective landlord should make sure the rent amount is in the plan or is supported by the debtor's current income, which would have to be more than the original income. Many Chapter 13s crash in the first year, or before they are completed, and are converted to Chapter 7s.

Check with the trustee or check the docket in the bankruptcy court to see if there have been problems.