There aren't doubts about its safety, and reading about it a lot, I am not convinced there ever were that were based on data - seems they all had to do with scare tactics.
In the USA it was available until 1991 with not a single medical case against it - and again since 1994 (simultaneously considered "safe" on its own but "not enough data to classify as safe" as an additive).
Not to mention, it has more than a thousand year of use. See wikipedia[0] about history and also the part of "controversy".
Unlike the egg/cholesterol and salt intake recommendations, which appear to be grounded in scientific incompetence, any concerns about stevia seem to be strategically managed by a competitor.