It's refreshing to see an optimistic hope for people. In my Empirical Engagement (Thinking Like A Scientist) we discussed how people come to believe the things they believe, and how we can't really trust people to look at things with a healthy dose of skepticism. Jefferson here has hope that people will use their "intelligence & faithfulness" to carry them through social interaction. He believes in them because they're using their knowledge to their advantage by applying, as he knows they will.

It is interesting to note that all these subjects, so succinctly explained here, are all under the umbrella term "Physics" now. During Jefferson's time, there probably wasn't a standard of learning to follow, so he had to list out the specifics here. We've come far in that now mentioning to physics to someone with some schooling will mean them considering some of these things instead of just "the doctrine of Physical objects of our senses."

Jefferson, though he was religious, was also a practical man. His Bible consisted of all the gospels except for redundancies and miracles. He essentially compiled a list of all the Bible's empirical data and used it in his personal life (hence why most people didn't even know about it--it was mostly for personal use). Here he attempts to bridge the gap between church and state, which he must believe should have some relationship. Any religious person would want their religious values to be reflected in government, even if they say they think church and State should be separate. This only means that Jefferson believed that the state should not influence the church, as the church is pure and holy and must only be directly influenced by God. When he says that this doctrine is the lovechild of church and State, he means to acknowledge and strengthen the relationship between church and State.

Jefferson's claim that all sects of religion stand on equal footing in accordance to the "principles of our constitution," is directly opposed to his sentiments about the religious sects of the Native Americans and African Americans. It's quite possible that Jefferson meant all sects of Christianity, as "religion" is singular. If so, would that mean that the freedom of religion described in the constitution implies that freedom of belief (so long as the central belief is Christianity) was what the Founders really meant? Even though Jefferson's religious tolerance here seems lenient, but then he talks about the Natives' "barbarism and wretchedness."