Unless you're going through _all_ the source material yourself, and making educated judgements on the quality and implications of the data, I don't think you can ever claim there's "overwhelming evidence" for any side, especially if the topic is controversial. If you're consuming information through secondary sources, basically every source will look at subsets of the data, will misinterpret data, and will have a bias, either intentionally or unintentionally.
Note that my response here does not rule out being skeptical over particular claims for definite reasons, only the blanket use of "Unless you're going through _all_ the source material yourself..." (your emphasis on 'all'.)
And why stop at source material? We know there is a replication crisis in science (the open discussion of which has, somewhat ironically, encouraged a wave of blanket dismissal of science), so surely this level of skepticism can only be assuaged by personally verifying all the original sources?