Using birth control should not be a problem at a “trad” or any other parish, because it is none of the other parishioners’ business. This is not for them to judge. Only the confessor should have access to this information. Besides, it is this gentleman’s wife who uses it and the gentleman does not agree, but it is permitted by the Church for him to have relations with his wife, and it is not sinful for him if he meets certain conditions.
The document addressing this can be found here:
catholicculture.org/culture/library/view.cfm?recnum=93
#13 down the list is the part which addresses this. The document gives guidelines for Confessors in marriage situations. It is very interesting and informative.