For someone like him I would assume he must have found something, especially with all the time and work he invested in it. Yet whenever the topic goes to Newton's work in that field no one ever mentions how exactly he contributed, just that he did, and even reading his Wikipedia page I don't find anything talking about any actual "breakthroughs" (if you can describe it as that) that he made in religion.
Newton's interests in theology are not nearly as interesting to us today as his work in science, which is one reason even framing them as "breakthroughs" feels strange. Let me give you an example of the kind of thing he thought was interesting. In Hebrews 1:8-9, it says:
therefore God, even thy God, hath anointed thee with the oil of gladness above they fellows.
Newton underlined the thy God, above, and saw it as showing that "therefore the Father is God of the Son as God." He considered this the "subordination of Christ." This is a theme he continued on, the idea that there is a distinction between "God the Father" and "God the Son," an issue he believed called into question the status of Christ and the reality of the Trinity. Newton spent a lot of time on exactly this question, the relationship of Christ and God, and the unreality of the Trinity.
Heretical stuff, for 17th-century England. But would we call this a "breakthrough" or just "an interpretation (however valid) of Biblical text leading to the embrace of one strand of Christianity over another." In Newton's case, he started with a background of anti-Trinitarian Arianism, and ended up becoming more and more convinced of this.
The fact that he kept all of this secret (and really needed to; he could have easily lost his job, and potentially his head, for such beliefs) means that essentially nobody knew his beliefs on these matters until relatively recently, so it is hard to talk about him making any real "contributions" to theology. He didn't influence anybody or anything in this realm. Whether he made legitimate "discoveries" or had significant "ideas" will probably depend on how interested one is with this line of questioning, and how sympathetic one is to his conclusions or their import. With religion, especially the private religion of someone who keeps their beliefs secret, it is much harder to make such arguments than it can be for something like science, where we can say with some greater confidence, "ah, this idea was the more correct idea," in a way we really cannot with this.
For me, the fact of Newton's extreme religiosity, and the fact that the above questions consumed him as much as questions about science did, and the fact that he felt the need to keep them secret, just about exhausts how interesting I find the topic. The minutiae all look like very repetitive and — to me, a non-believer — totally uninteresting theological concerns that primarily make sense in a context of religious political uncertainty.
If you want to delve into Newton's religious writings, see esp. chapter 8 in Richard Westfall's Never at Rest: A Biography of Isaac Newton, from which the above examples were all taken.