OTL events that get missed:
-Scotland might not win at Bannockburn and thus could be more integrated into England in the 14th/15th century, word was some of Robert the Bruce's men at the battle were Templar holdovers
-Switzerland as we know it might not exist for the same reason
ATL possibilities:
-Templars head for Constantinople and work for the Emperor in exchange for spreading the word and gaining lots of trade rights, eventually even coming to own whole cities within the Empire. Constantinople still falls but much more slowly, a la 1600-1650, and the Renaissance is delayed by half a century as a result
-Templars bankroll expeditions around Africa a century ahead of Columbus and work closely with Henry the Navigator, eventually leading to a landing in modern Brazil in 1422 with circumnavigation of Africa in 1435
-Black Plague wipes out many of the order as they work to help the natives and their own assets are largely wiped out, local kings do the rest a generation later
-Templars eventually become a military asset of the Papacy itself and help it unite southern and central Italy by 1450, eventually uniting the peninsula with Corsica, Sardinina, Sicily, Crete, and much of Greece by 1500. Templars then become the financial and commercial arm of Rome with assets all over Europe
Just some thoughts...