I don't have concerns about him making the Empire more Sigmarite, it's making the Empire less every other religion that I'm worried about. In canon, he pushes an agenda of pushing Sigmarism at the expense of other faiths, and if he antagonises the other Cults, that could have repercussions on the Colleges as a whole. Additionally, the official stance of the Grey College for its members faith is "secular tolerance". If he replaces that with institutional Sigmarism and tries to restrict the worship of other gods within the Order, then that is very relevant to us, because a) we're a devout Ranaldian, b) we believe in freedom of religion, and c) we're currently working with and building ties with a minority who have been oppressed by followers of Sigmar, possibly with the intent of recruiting them. If Patriarch Starke undoes all our, Kupfer's, and Kurtis's hard work with the hedgewise because they won't worship Sigmar, I'm going to be very upset.
Just because we're likely to be half a continent away from him doesn't mean his actions aren't going to affect us. Besides, who here who voted to tell Algard about the Lord of Change would have voted to tell Starke? I don't think I would have—I trust and respect Algard a lot, and that fed into me voting to tell him about the demon. I don't have that level of trust in Starke. Also consider that we only really know two things about him—he's very good at destroying Chaos Cults, and he's "way too into Sigmar". Frankly, I'm not comfortable with that level of information, and I'd rather know more about him as a person before I trust him as our boss, even if he can't effectively micromanage or otherwise control us.