It is not known what customs are referred to. Perhaps the reference is to the fact that although the Romans recognized the Jewish religion, they did not permit them to go about actively seeking converts. In the eyes of the Roman officials Paul and Silas were at best Jews seeking converts for their religion.

Teaching customs that are against our law may be rendered as “teaching us to do things which our law says we should not do.”

We are Romans is rendered in some languages as “we belong to the city of Rome” or “we are the same as people who live in the city of Rome.” (See also 16.37.) And cannot accept or practice them may be rendered as “therefore we must not do as these men are telling us.”

Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on The Acts of the Apostles. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .