If you were a member of the sanctioned church (almost invariably Protestant–in Virginia it was the Church of England), then, yes, you got to do those things. Otherwise, you often had no vote in government, could hold no public office, could not hold public religious services, your clergy could be criminally prosecuted, you had to pay taxes specifically to support the state church and often had to attend it or pay fines, purchase or inherit land, educate your children in your faith, etc.
You need to do a little more research into the situation for religious minorities that existed in colonial America, especially for Catholics. I know in NC, Catholics were not allowed to hold public office until well into the 1800s. The ideal of separation of church and state was not instant, but has been a long hard road with the need to guard advances every step of the way against groups that would encourage a return to the “good old days”.
Catholics have a very great deal to be grateful for about America’s ideal of the separation of Church and State, even though the application of such is not always ideal.
I commend to you the context of those remarks
yale.edu/lawweb/avalon/jevifram.htm
traditioninaction.org/History/B_001_Colonies.html
*Few Catholics realize that in all but three of the 13 original colonies, Catholics were the subject of penal measures of one kind or another during the colonial period. In most cases, the Catholic Church had been proscribed at an early date, as in Virginia where the act of 1642 proscribing Catholics and their priests set the tone for the remainder of the colonial period.
Even in the supposedly tolerant Maryland, the tables had turned against Catholics by the 1700s. By this time the penal code against Catholics included test oaths administered to keep Catholics out of office, legislation that barred Catholics from entering certain professions (such as Law), and measures had been enacted to make them incapable of inheriting or purchasing land. By 1718 the ballot had been denied to Catholics in Maryland, following the example of the other colonies, and parents could even be fined for sending children abroad to be educated as Catholics.
In the decade before the American Revolution, most inhabitants of the English colonies would have agreed with Samuel Adams when he said (in 1768): “I did verily believe, as I do still, that much more is to be dreaded from the growth of popery in America, than from the Stamp Act, or any other acts destructive of civil rights.” (3) *
There is much more of interest in the article.