It is a meaningful constraint.
In general, a tactful interaction seeks to avoid offense to the extent feasible, often preferring a delay or compromise over the risk of aggravating the situation.
Other considerations could be time, concern for specific individual(s), professional/legal requirements, social pressures, or other personal responsibilities.
A good answer will address all constraints given the context, or, failing that, at least the constraints explicitly mentioned. If tact is not mentioned explicitly, it may be reasonable to prioritize other considerations.
This constraint should influence the answers.
Questions regarding tact prohibit responses that suggest impolite, aggressive, or uncommon/abnormal behavior--even if those suggestions are eminently more practical.
Tact generally seeks to prevent escalation. Sometimes escalation can guarantee a quick and certain resolution, but that may not be a priority. E.g., a dispute over property lines need not involve a lawyer.
In addition, this type of question opens the poster to the criticism that he or she is doing something rude and should therefore pursue a different goal. Rudeness is fundamentally incompatible with a tactful resolution.
And finally, it also allows users to downvote impolite or inconsiderate responses. These responses are explicitly not helpful when tactful answers have been requested.
Personally, I am inclined to suggest less tactful behavior on occasion or to upvote answers which do--particularly when a more tactful resolution appears unlikely. However, I will not do so if the question specifically asks for tactful advice.
shouldn't any question seeking an interpersonal solution be seeking a "tactful" solution?
Not necessarily. Sometimes you wanna phrase something in the most hurtful and demeaning way possible. Sometimes, you want to phrase it so that you are sure you get the point across, tact not being (as) important. But yes,tactfully
is usually the default, so missing any other modifier, I guess it could be omitted. But until that's standard (or close), I'd argue that the titles could lose some meaning on the edit. – xDaizu May 15 '18 at 12:17