This is quite different from the seventeenth-century view typical of people like Newton that science is part of religion, and that the scientific enterprise is an intrinsically religious pursuit.
very much yes
Really, science and religion have been mostly distinct since the nineteenth century
yes because the general science machinery is so good in adding insights and knowledge that find practical (engineering) applications, that it sets the stage.... a stage where "everything" we need is generated by science without any need for religion.
An unstoppable machinery at a steady succes rate without real limits except the amount of money/scientists/resources/time thrown in.
In a cultural sense Science is dominant since the 19th century
But also a bit "no" regarding the science of the ultimate understanding of the fabric and origin of our Universe.... the quest for the final fundamental laws of physics.... the ultimate physical truth
Here the feeling of "perhaps never knowing it all" starts to come in, the sheer awesomeness humbling the human existence
Heisenberg adding to our limited science position with his uncertainty principle: we cannot fundamentally know precisely.
Brought to the point by prof John Stewart Bell in 1964 in his "On the Einstein Podolsky Rosen Paradox" where he proved that Einstein was wrong (the determinism by fundamental laws and yet to discover hidden variables of quantum physics to get that deterministic as well) and we have fundamentally to live with a random universe.
=> Science is limited
Heisenberg, who was as you say religious, made the quote: “The first gulp from the glass of natural sciences will turn you into an atheist, but at the bottom of the glass God is waiting for you”
So my feel is that in the quest for our fundamental laws, the full divorce comes later than the 19th century, perhaps to the point around WW2, after Einstein, with indeed Feynman. And Hawkings is after that

The need to attach the unexplainable to God, the need to have fundamental science laws replace the creation in a deterministic way, was no longer there.