How could the continental congress approve this document when so many of its members owned slaves?

Because it will only effect their safety and happiness and even though everyone is equal they will still be discriminated.

Explanation:

It is true that many of Continental Congress members owned slaves but the reason they signed the documents opposing slavery is because it will make the slaves them feel happy and this will improve their perception of their safety in coming years and especially the safety and social status of their children. However, the members of the Continental Congress knew that they had the power to still keep them as slaves may be not in the form of slavery but in other ways and that they will still be discriminated even when slavery is illegal.