I'm a bit confused by your question. What rules/laws are you talking about and by what time period? On the eve of the American Revolution, 1775, church attendance and membership was at an all-time low across the American colonies. In the few places where puritan laws existed that mandated church attendance, most from the 17th century, were no longer enforced or even existed. Many historians have known and acknowledged that while most American professed to being religious, around 15% actually belonged to a church in 1775 and at most, 20% of Americans attended at least one church service annually.(1) This was significantly higher in parts of the south, such as South Carolina, which is estimated to have had around 30% church membership rates by 1775, the highest in all the colonies.

Did they have to go to church just like their masters did?

Almost no one was mandated to go to church. In some states, like Maryland, religious taxes were imposed on folks were non-Anglican, but this did not force them to go to church. (2)

I know that lots of indentured servants were poor people from Ireland, many of whom I assume were Catholic, but colonial America was pretty hostile to Catholicism.

Irish, yes, but not exclusively. Also, indentured servitude was on the decline by 1776. Indentured servants also came from poor parts of of Scotland as well. But your comments about Anti-Catholism in the colonies is well-founded. This became a real problem for Catholics, especially in Colonies that originally had high Catholic populations, like Maryland. But Catholics were forbidden to own churches prior to Marylands Constitution of 1776, so they could not attend church services. Wealthy Catholics, like the Carroll family (led by Charles Carroll, who represented Maryland at the Constitutional Convention and was a signer of the Declaration of Independence) fought hard for Catholic rights through that era.

Did they attend Anglican (or Dissenter) services?

None were forced to. Again, taxes to support Anglican clergy were imposed.

Another quirk of the southern plantation system was how far apart people lived from each other. Did planters simply have private services in their homes?

Some did. Charles Carroll's father was known to host church services in his home during this period. But yes, across the colonies, not just the south, many people lived far from their neighbors. The census of 1790 shows that 95% of Americans lived outside of towns or cities, that's part of what attributed to such low church membership.

Again--how could the authorities "keep track" of this? I know some planters in South Carolina had a second house in the city, so would they go into town every week? (But if that's the case, what about their slaves and servants?)

As stated above, there were no "authorities" who could impose such penalties. Many American gentry did own houses in some towns, but not all. If they did travel into town, they would typically be accompanied by servants or slaves, but most slaves did not attend church services with their owners. Instead, many slaves, especially on large plantations, held their own church services on their own.

I hope this makes sense. Please let me know if this makes sense or if you have any follow-ups.

1). Jon Butler. "Magic, Astrology, and the Early American Religious Heritage, 1600-1760" The American Historical Review, Vol. 84, No. 2. Apr., 1979, pp. 317

2. Jon Butler & Grant Wacker & Randall Balmer. Religion in American Life. Oxford University Press. New York. 2008. Pp 145