It's complicated! On the one hand, you had the troops in New England burning the pope in effigy. OTOH, you had Catholics at the Continental Congress, and widespread Francophillia. Washington also attended a Catholic mass as a show of ecumenical unity during the Constitutional Convention, which he wouldn't have done if it was considered horrible. (This is a man who shunned controversial gestures all the time).
True, anti papism was not policy, but the views were very common among the populace, especially in New England (and in England it was official policy still), the annual burning of the pope in effigy had been done before the war and for a long time. The founder are interesting in this part, since many of them were English rite Masons, and thus had a very specific view on religion.