Eh, I throw down the same challenge to what people say in this thread. Source it.
Templar Navigators I can kind of see even in a Black Templar environment - I get the impression that Navigators are fully aware of how indispensable they are, and kind of don't give a rat's *** what anybody thinks of them. If a Navigator House provides service to the Templars, I'm sure it's either (i) for that House's own damn good reasons, and/or (ii) because even Black Templars know enough not to piss off the people that make their fleets go.
As for other psykers, such as astropaths, I think there's two plausible options here. The first is the same as for Navigators - that while Black Templars may not like them, they know better than to piss off the people that let keep the chapter together. Even sanctioned psykers in other branches of service are used to being around people who don't like them, and they seem to find ways to cope. The second is that the Black Templars draw exclusively from psykers who themselves view their powers as unholy abominations, and choose service with the Templars as a form of penance for their very existence. We know there are plenty of psykers who hate what they are, and choosing the discipline of service with the Templars strikes me as a very Imperial mindset.