Why can't I hire the Knights Templar?

Solution 1:

If a Holy order is busy fighting a war in personal capacity i.e. in your case, this crusade as thegrinner suggested about three years ago, then they aren't available to be hired by other rulers.

They are already a co-belligerent in the war so employment by any ruler in midst of that would cause internal logical errors. Who gets their war contribution score?

You can easily check that in the list of participants of the crusades. An easy way to overcome this is make up your mind early enough. As soon as crusade is declared, send a missive to the pope with request to join him and hire the available orders before someone else does or before they decide to get busy themselves.