Are you for real? Based on what Anders and Wynne tell us they do it. They exploit love or anything dear to mages to control them. I have my doubts if every single Templar does that (obviously) but they are our only source.
Wynn doesn't tell us they exploit the relationships of mages: Wynn tells us they try to prevent the mages from having relationships. Those are two different things, and can not be used interchangeably. Anders, on the other hand, tells us many things, a number of them false, but the only substantiated claim of exploiting a pre-existing mage relationship I can think of with regards to Anders was the use of Karl as bait to catch Anders. Which was done by Alrik, and has never been raised as a standard practice.
I don't go around ranting about what Templar order is "suppose" to do. When did you ever see an order like Templars doing what they are supposed to do?
Quite frequently. It's kind of what separates professionals from amateur organizations.
So far the canon of the game tells me the Templars do exploit the love and relationships between mages. Unless a dev tells us what Anders and Wynne said are lies its canon
Perhaps we would be better suited at identifying what in partiular is said that you believe indicates exploitation as opposed to something else. For Wynn, I simply do not recall her claiming any such thing- being denied a relationship and her child, yes, but nothing in a sense of exploiting for control. No 'we have your child, obey or else.' No 'we know you like this person, do as we say or something bad happens to them.' That is exploiting a relationship to control someone.
Anders already lies (and hyperbolially exaggerates past reality and is sometimes simply mistaken and just plain wrong) enough that his claims are already deserving of scrutiny: he is not an objective or authoritative source. This, to, deserves examing what instances in the canon of the game show the Templars exploiting the love and relationships between mages to control them. Even Karl wasn't exploited to control Anders: Karl was bait for a trap, not a hostage to Anders good behavior.