The unanimous opinion in Castro v. Scanlan is here. It’s worth noting the appellate court only reached the standing issue. It did not address the political question doctrine issue, which I noted here that the district court reached. And from the opinion (lightly edited):

. . . we cannot define a “direct and current competitor” in the political context so loosely that a claim of political competitor injury becomes a means by which a federal court entertains a suit based on what is, in effect, a generalized concern that a particular individual is not lawfully entitled to run for office. We must define such a competitor in a manner that ensures that the plaintiff who claims political competitor standing has “[t]he requisite personal interest,” in the determination of the constitutionality of a rival candidate’s eligibility for office in consequence of a “concrete, particularized ‘injury in fact’ over and above the abstract generalized grievance suffered by all citizens . . . who (if [the plaintiff] is right) must live in a State subject to an unconstitutional” electoral process.

. . . no authority of which we are aware — or that Castro has identified — suggests that the mere statement of an intention to seek write-in votes suffices in and of itself to make an individual a “current and direct competitor.”

. . . Thus, because a plaintiff incurs the kind of competitive injury that grounds Castro’s assertion of standing by actually being a putative rival’s competitor for either votes or contributions, we cannot agree that a showing that a plaintiff has taken the steps required to be placed on the ballot in the primary contest at issue necessarily always suffices to show such an injury. Indeed, if the rule were otherwise, then the theory of political competitor standing would seem to offer those invoking it a significant means of effecting an end-run around the usual bar to a federal court’s power to remedy what is in the end merely a generalized grievance. For, under a rule of that sort, plaintiffs would be permitted to secure standing without adequately distinguishing their interest in the legal outcome of the case from that of anyone in the same state who is interested in ensuring legal compliance with that state’s ballot access rules for candidates.