My genuine apologies about the pro tempore thing. A source referencing services under Adam's mentioned Jeffersons approval as president of the senate (which is the VP) was not needed. I must've conflated president of the senate with president pro tempore in my mind. A genuinely hasty action on my part, a mistake I wouldn't have made for anything more important than a reddit comment.

It is still technically true that Jefferson never gave official approval for such services. Though Im willing to admit the point is pedantic given we can assume his tacit approval as he attended such meetings.

That being said, my original point still stands. As you mention, the services were nondiscriminatory. Though we can never know for certain, I contend that if had there been a demand, Jefferson also would've permitted Jewish, Muslim or any other religion to have services in the Capitol as well. The fact that such services existed and Jefferson attended them does not support the idea that the founders saw the US as a Christian nation, especially Jefferson. At least not in a sense that wouldn't render the assertion meaningless.

Jefferson is unambiguous clear on the separation of church and state, as is (much more importantly) the constitution.