How does secular or atheistic Buddhism relate to Buddhist Modernism?
The existence of deities is kind of orthogonal to it. It wasn't really a question that most of the leaders of this movement were very interested in. I don't know what 'secular Buddhism' is but it sounds depressing.
That's at best a strongly Theravadin view that entirely discounts the Mahayana tradition's insights into what Shakyamuni did and did not teach, and at worst an outright misconception, similar to the misconception that he didn't teach literal transmigration of souls. The sutras present him in conversation and argument with people who
did deny the existence of deities and souls. Buddhism elaborates the concept of dependent arising partly as a way to provide a 'scientific' (in the broadest sense of the term) account for things like deities and souls that
doesn't involve denying their existence. There is not a single Buddhist tradition of which I am aware that is in fact atheistic. At most they don't purport to address the question.
It needs also to be reminded that the average South or East Asian person's conception of what a 'god' is is, or historically was, not ours.
The idea that 'add-ons' are definitionally undesirable or would inherently not be approved of by the religion's founder is also itself one that I think is a lot less obvious than a lot of popular discourse about religion, especially in societies that pay lip service to the ideals of the Reformation, would have us all believe.