I really think too many people are reading too much into the allies matrix, especially in terms of converting game mechanics into background.
Black Templars being Desperate Allies with Battle Sisters basically means that if they're deployed very close to each other, there's a chance of units not doing anything for a turn - probably because they're having some intense ideological discussion about the true nature of the Emperor's Divinity. the Templars, being more fanatical than most chapters, are more likely to get into such an argument in the middle of battle than other chapters, who are Allies of Convenience. It's not that they're more friendly with the Eldar, it's more that they're not likely to have these arguments with the Eldar, because both sides know that as soon as the common enemy is dealt with, the Black Templars are going to start firing at their sometime-allies.
The allies matrix is just a set of game mechanics, it's not a political map of the 41st millennium