Your potential landlord wants to be sure he / she is protected by getting the best possible tenant for their property and protecting their investment. You want to make sure your information remains private. Both understandable. Talk your agent (if you are using one) and express your concerns. If you are not using an agent talk to the landlord direct. They may accept your information with some items blacked out. A credit score does not give any detailed information . Sometimes landlords will also ask for a criminal background check.
All the best,