Is that an accurate statement? I have never heard that included in the definition of separation of church and state. Sounds wrong.
If you are funding a political campaign (not just any political speech, but an actual campaign) you have to be set up as a political campaign rather than a church.
> 1954, Congress approved an amendment by Sen. Lyndon Johnson to prohibit 501(c)(3) organizations, which includes charities and churches, from engaging in any political campaign activity. To the extent Congress has revisited the ban over the years, it has in fact strengthened the ban. The most recent change came in 1987 when Congress amended the language to clarify that the prohibition also applies to statements opposing candidates
https://www.irs.gov/newsroom/charities-churches-and-politics....
In practice, churches are given quite a bit of leeway to engage in what any reasonable person would call political campaigning.
The statement is correct there but it’s not a constitutional thing it’s an IRS thing.