Do not use Bar Keepers Friend Soft Cleanser on marble. Bar Keepers Friend explicitly says it does not recommend Soft Cleanser on marble, while the product contains oxalic acid, citric acid, and a glass-oxide abrasive.
Why marble makes this a clear no
This is not just a generic caution. The manufacturer advises against using this product on marble, and the formula combines acidic ingredients with an abrasive. Marble is vulnerable to both acid etching and surface scratching, especially when polished.
If you already used it
Rinse the surface thoroughly with clean water and dry it with a soft cloth. Do not keep scrubbing a dull or hazy area. If a visible dull patch remains after drying, the finish may have been etched or abraded and may require professional refinishing.
Safer approach
Use a pH-neutral cleaner intended for natural stone or another cleaner specifically approved for marble. Bar Keepers Friend itself points marble users to its pH-balanced Granite & Stone Cleaner & Polish instead of Soft Cleanser.