This question is regarding the Johnson Amendment. Suppose that a 501(c)(3) does not specifically endorse or oppose a candidate, but rather has a biased narrative regarding the candidates. At what point would this reasonably violate the Johnson Amendment?
There is room for interpretation. The Congressional Research Service issued a paper in 2013 which restates what it found the law to be. However, there isn't a corpus of publicly available cases which test the limits (post Citizens United or otherwise). There seems to be a private letter from the IRS (redacted) where such a status was revoked for political involvement.
The CRS analysis article repeats the statutory law which prohibits
"participating in, or intervening in (including the publishing or distributing of statements), any political campaign on behalf of (or in opposition to) any candidate for public office,"
and then comments that the law "does not further elaborate on the prohibition". Moving on to the regulatory language from Treasury, they observe
As to what types of activities are prohibited, the regulations add little besides specifying that they include "the publication or distribution of written or printed statements or the making of oral statements on behalf of or in opposition to such a candidate.
which is just a restatement of the unclear statute. They note that
organizations are allowed to conduct activities that are political in nature but are not related to elections, such as lobbying for or against legislation
may engage in certain election-related activities so long as the activities do not indicate a preference for or against any candidate
Whether such an activity is campaign intervention depends on the facts and circumstances of each case.
For instance, voters guides are supposed to be unbiased, and
there are numerous ways in which a guide may be biased, and the determination will depend on the facts and circumstances of each case
Issue advocacy is clearly allowed but
the line between issue advocacy and campaign activity can be difficult to discern.
In some rare instances where all candidates advocate the same position on an issue, issue-advocacy is not a surrogate for candidate advocacy. The report indicates that the IRS has studied the general question, but the IRS reports are no longer available through the IRS, but if this is the 2006 report, no specific details are revealed (which would lead to discerning the extend to which issue-advocacy can substitute for candidate-advocacy). In short, there is no way to know what is allowed versus prohibited by the IRS.