The 1st Amendment quite clearly restricts our legislators from making any law "respecting an establishment of religion".
Agreed, religious men are free to "influence" [urge/induce], but officials sworn to support the Constitution are not free to make law based on or 'influenced' [caused] by any of the establishments of specific religions.
That is completely false, and to restrict anyone from legislating because of their religious morality is a "religious test" forbidden by the Constitution.
Any religious test is forbidden to qualify for an office, but after attaining office, the official must support the Constitution, - including the 1st Amendments restrictions on the various 'establishments' of religions.
The first amendment restricts the establishment of a national religion, it does not restrictlegislators from making law "based on or 'influenced' [caused] by any of the establishments of specific religions." The amendment simply does not say this and has never meant this.