In this extended fight scene, there is no rousing music to accompany the action. The only sound is that of grunting men and clashing swords. Did they possibly want to show "reverence" because they were in a convent? Personally thought it was a nice touch.
Anti-religious? No more so than Dumas' original novel, which was not anti-religious in the slightest, except maybe for some anti-Jesuit sentiment with Aramis, but then anti-Jesuit is not anti-religious.
Lester does veer negatively upon religion. It is portrayed as deceptive: Aramis tricks a guard into prayer to get a shot at him. Milady dresses in a habit to trick Constance (in the book, it is Constance who is in the habit). It is portrayed as causing a mountain out of an anthill: Porthos asks Aramis if the war is really about the disagreement of reading the Bible in Latin or French. Aramis replies that such things are what religious wars are about. At one point, D'Artagnan skewers a lectern. A rosary is used as a murder weapon.
Almost everything you just mentioned comes straight from Dumas.
Milady first pretends to be a Puritan in order to deceive Felton, and then she pretends to be a nun because Constance is being held in a convent and that was the only way to get in. But, in this case, the point isn't 'religion is bad' the point that Milady is bad because of the way she stoops to manipulating religion. In the novel, Milady actually is Catholic, and so Lord DeWinter has Felton bring her a copy of the Roman missal. When she notices that he seems to be disdainful of the missal, she seizes upon it and pretends to be a Puritan. Lord DeWinter even calls her on her BS basically asking 'since when were you a Puritan?'
To put it another way, the fact that she is capable of this kind of deception means that she is pure evil and capable of anything. That is why they decide that she needs to be killed. The entire point is that what she is doing is an outrageous blasphemy, this proves just how bad she is, that she respects nothing.
Tell me. have you read the novel this movie is based on? These movies are the most faithful adaptation of Dumas' novel that have ever been made (at least in the English language anyway), and there is a bit of a satirical and ironic tone to the novel at times, which these movies reflect. Many people don't like the humor, but the humor is present in the source material.