Should making a donation, campaigning for a candidate, or exercising other forms of political speech disqualify one from working as a civil servant?

No, but it just raises valid questions regarding motivations. Civil servants are supposed to not be biased toward a particular political party. In practice, that may well not be the case, but questioning his appointment is fair enough. The Tory party has for many years attacked the BBC, using those attacks as a political tool. So people draw conclusions from the appointment of a prominent Tory donor to the post of DG.