The common good, responsibility to shareholders, and political activity
Nonprofits, he says, get many tax benefits because they work for the common good. If they were to get involved in electioneering or major issue advocacy, they would be pursuing a narrower partisan benefit, and thus would no longer deserve the tax benefits they're given by society. This seems to me to fallaciously inflate the civic sector and denigrate politics. Think, for example, of the Roman Catholic church in the US. The church's core activities, which justify its nonprofit status, include things like administering confession and communion to parishioners. But this seems to me to be a narrow, partisan activity. I don't see how I (a non-Catholic) or the wider society benefit from these rituals. They may certainly be good for the individual Catholics taking part in them*, but it's a stretch to say they serve the common good of society. On the other hand, some of the church's political advocacy -- for example, its backing of comprehensive immigration reform -- seems to me to do much more for the common good, since the US as a whole (and sender countries like Mexico) would benefit from a more just and humane immigration system. Even the dread electioneering can serve the common good, perhaps even better than direct service to parishioners, if the candidate in question is likely to institute good policies. This is not to say that politics is never narrowly partisan, or that all nonprofits would do more good by becoming advocacy organizations. But I do think that the political-nonpolitical line is a poor fit for the partisan-common good line.
He makes a related argument against corporations getting involved in politics. A corporation's purpose, for which it has been given special treatment in the law, is to make money for its shareholders. If a corporation is turned into an ideological political apparatus, those shareholders have been betrayed and the corporation has lost the justification for its special treatment. This argument is generally right, but it wrongly conflates all political activity with political activity serving an ideological mission unrelated to the corporation's business plan. In fact, much corporate political activity is part and parcel of its money-making activities. AN oil company campaigning to open ANWR for drilling is not misusing its shareholders' money on an unrelated crusade, it's furthering its profit-seeking by trying to change relevant government policy, with a net payoff for shareholders if it succeeds.
*Some atheists may go farther and say that these rituals are a waste of time and effort, and that the church is creating new needs (by preaching about the need for forgiveness to avoid damnation) and then fulfilling them, resulting in no net gain for society. I think my argument works fine with the more religion-friendly take on things in the main body of the post.