Is this issue an absolute litmus test for a candidate for public office?

Answer 1

No. Litmus tests are opinions - when we speak of a litmus test, we are talking about a person's opinion about the candidate's suitability for the office. As with all opinions, there are no absolute truths - that's why they're called opinionsand not facts.

In most Western countries, candidates for public office generally only have two requirements: they be citizen of the country, and are mentally competent. For some offices, a specialized education may be required (i.e. in many European countries, a law degree is required for any judge). And in few cases, conviction of certain crimes will make a person ineligible.

A funny quirk of the US system is that you don't actually have to be alive to be elected to a public office. In cases where a candidate has died after a ballot has been printed (or, in some cases, after a primary election has taken place), it is entirely possible for that (dead) person to be elected to the office. In that case, the office is then treated as if the holder (new electee) had died while in office, and a successor is then named as per normal for death-in-office.