At the end of the first game, the immediate Templar threat has been dealt with so that they have no longer become a major concern for the Assassins. They are mentioned in Altaïr 's journal, but for the most part, he has moved on to a new, greater ideological enemy: religion itself.
He compares the old pagan religions with what would be in his time more modern religions. He concludes that the older ones displayed a thirst for knowledge in their believers, that those religions attempted to "categorize study, explain, and understand how things work -- even if it was flawed". But he has nothing but disdain for the modern religions:
Now we are asked to succumb to a far more simplified explanation. How naïve to believe there might be a single answer to every question. Every mystery. That there exists a lone divine light which rules over all. They say it is a light that brings truth and love. I say it is a light that blinds us -- and forces us to stumble about in ignorance . . . I long for a day when men will turn away from invisible monsters and once more embrace a more rational view of the world.
He sees proof against these monotheistic religions in nature, commenting on how survival demands the death of another. Finally, he describes how the Assassins are growing larger and the reasons for which these new recruits join:
Each tells a similar story -- of having discovered the first part of our creed: that nothing is true. Too often, though, the revelation undoes them. They lose their morality, certainty, security. Many are driven mad. We must guide them. Help them to heal. Their minds must not be filled with more fairy tales, but with knowledge instead. Let them have answers -- and let those answers be difficult and complex.
It is interesting that people are not joining the Assassins to become killers; they're joining the Assassins because among them is a community that shares their newfound belief, or lack thereof. The Assassins are acting more like a relief center for those that lose faith in god than they are actual assassins because killing isn't actually their main goal. Their main goal is ideological, to educate the populace with knowledge instead of faith; if that happens to demand the death of someone, well, they happen to be well equipped to handle it. Their title of "assassins" is actually a misnomer since killing isn't their end game.
Fast forward to Ezio's time, when Assassin's Creed 2 actually takes place, and the Templars are once again a major threat. Because the games themselves revolve around the animosity between these two groups, it's easy to assume that the Templars are the only sworn enemies of the Assassins. They are, of course, sworn enemies, but the Templars are just a small part of a larger whole. Their goals may be more selfish than the goals of most religions, but their means are the same: they encourage faith to gain power, while religion in general encourages faith as a means of salvation. The Assassins fight against the establishment of faith in whatever form it takes; the Templars are just an effective face to put on that vague enemy.
And yet, the Assassins are also practitioners of faith. They have faith that what they do really is best for the common good. In some instances, this idea can be immediately proven: they kill a murderer so that he cannot murder again, but the long term consequences of their political meddling are unknown. All they can do is hope is that it is all for the best.