When the oppression takes the form of "not letting the party in question do horrible things to other third parties", then... yeah. They deserve to have that part of their platform oppressed. The same way "intolerance of intolerance" is okay, and how the whole Sharia Law "execute heretics" thing is something most people would be okay with suppressing, religious freedom or no. The same way we have freedom of speech, but you're not allowed to threaten someone into giving you all your money, and we have freedom of association but you aren't allowed to conspire with people to break the law. They deserve to be oppressed the same way the modern day religious right deserves to be "oppressed" by the fall of the DOMA.
(Not that this was the part that was actually being oppressed, Church of England was dicks and haha, that was practically the only part they thought was a right good idea)
And there were lots and lots of other non-terrible religious folks moving around everywhere trying to do their best to avoid persecution. The Quakers, who the Puritan's seemed to have a hate-hard-on for, were all-around pretty damned awesome for example.
And as far as the "different from the modern American right", yeah - I'm sure my ancestors would have a lot harsher language for them, from personal experience, and the modern American right doesn't advocate a good murderin' of heretics as the primary purpose of their religion. (Hint: It's in the name! Puritans believed in "purifying" the church by getting rid of everyone who disagreed with them)