You will be permitted to land on Ascalon from Welcoming or Friendly. Can't remember exactly, but above 30 relationship anyway.
Also, the only real way to gain friendship with them is to participate in Crusade, and kill any units besides Templares, in the system that currently has a Crusade. The more units you kill, the better.
As a note, while participating in crusades starts out being a good way to get templar reputation, it does eventually fall off; kill counts that used to net +30 reputation start giving only +3.
At that point, the best option is to fight enemy fleets near Ascalon (which has the side-benefit that there's no risk of pushing your rep with other factions below -75). You can sometimes lure fleets over there, and every so often (if you're using Templar with SS+) the church of Ludd will send a "purification fleet". Fair warning: the purification fleet always has a supercapital flagship with combat 10. Which means it will slowly regenerate hull towards 50%. Which means you need to bring a fair amount of firepower in order to burst it down in the brief window while it's venting. My standard Shadowyards Mimir loadout only just barely meets that firepower requirement, so if you're one of those players who likes trying to kill everything with a Medusa... good luck?
Aside to Dark.Revenant: The purification fleet was a fun fight the first time. Okay the second. And really kinda tedious after that; the Luddic supercapital isn't particularly threatening, since it's so easy to back off and vent; just make sure to time it for right after the main gun fires. Not sure if you can do this, but I know you have some mechanism for random variants - it would be kinda neat if the purification fleet made much-more-common-than-normal use of scavenged templar weaponry or even the occasional ship.
I'd also suggest increasing its frequency, and/or making it recognize when it's lost most of its power and should go home - had a few times where it spent ages flying around with just a few surviving non-combat ships or fighter wings. And the really tedious part of grinding up rep with this isn't the battles, but waiting for a new purification fleet to get sent out after you smashed the old one.