The Churchill report generally seems very thoughtful and scholarly, but it does have a small error (which commenter DelVerSiSogna also caught). The report states (p. 4):
To use an analogy, a motorist who is stopped and ticketed for speeding because the police officer was offended by the contents of her bumper sticker, and who otherwise would have been sent away with a warning, is still guilty of speeding, even if the officer's motive for punishing the speeder was the offense taken to the speeder's exercise of her right to free speech. No court would consider the improper motive of the police officer to constitute a defense to speeding, however protected by legal free speech guarantees the contents of the bumper sticker might be.
In fact, the First Amendment rule, as set forth in Wayte v. U.S., 470 U.S. 598 (1985), is:
"Selectivity in the enforcement of criminal laws is . . . subject to constitutional constraints." In particular, the decision to prosecute may not be "'deliberately based upon an unjustifiable standard such as race, religion, or other arbitrary classification,'" including the exercise of protected statutory and constitutional rights [such as free speech].
Even prosecution of people who are guilty of a nonspeech crime might thus violate the First Amendment if the government deliberately selected them for prosecution because of their constitutionally protected expression (though I should note that this is a very tough claim to prove).
Nonetheless, whatever may be the rule for criminal prosecutions triggered by the policeman's own hostility to the target's speech, such a rule need not be applied here. This isn't a criminal prosecution, but the university's decision whether to keep someone on its faculty; it need not keep a dishonest scholar on board, even if the complaints about the scholar were motivated partly by the complainers' hostility to the scholar's viewpoints. And as best I can tell, there's little reason to think that the University wouldn't have investigated Churchill had he been accused of the same misconduct but had expressed diferrent views. These are serious charges, and my guess is that most universities would indeed look into alleged multiple falsification of evidence and plagiarism by their faculty members.
There was a connection between Churchill's politics and the investigation, but it seems to me much more attenuated than in the bumper sticker context. Churchill first attracted public notice because of his "little Eichmanns" comment. This led people to scrutinize his work, and past critics of his to repeat their criticisms. This in turn yielded the large body of accusations, large enough that the University had to take notice (in a way that it didn't seem to have done when at least one of the accusations had been separately brought to its notice some years before). So the better analogy is if someone had caused a lot of controversy by his bumper sticker; this caused a lot of people to notice him, and in the process to notice that he was speeding; they in turn complained to the police officer; and the police officer gave him a speeding ticket. There, I think there's no problem under Wayte; the government official (the police officer) wasn't making the enforcement decision based on the bumper sticker, though the people who complained to the officer -- private parties who have no viewpoint-neutrality obligation under the First Amendment -- were motivated by the bumper sticker.
As the report points out, "public figures who choose to speak out on controversial matters of public concern naturally attract more controversy and attention to their background and work than scholars quietly writing about more esoteric matters that are not the subject of political debate" (p. 4). That seems to me to be exactly what happened here. Unfortunately for Ward Churchill, it turns out that his scholarship couldn't bear the attention that his statements prompted.