Doesn't red lyrium just give you power and turn you insane? How can it brainwash?
There are codex entries about what happened to the higher ups that started suspecting foul play from Lucius and his chums that you find during COTJ. They were killed.
I'm sure that there were templars in the rank and file that agreed, but it wasn't unanimous. The ones that were hooked to red lyrium were brainwashed in a way though.
I wouldn't call them brainwashed. It just muddies the issue. I would say they were addicted and corrupted, however.
Ultimately, everyone already admits that the new Templar leadership as of COTJ joined Corypheus for the power he was offering. Some of them did so because they were insane, like the Lord Seeker, some did so because they wanted it. The rank and file are split between those that followed orders and were themselves corrupted, and those who suspected something was up and ultimately rebelled.
I haven't read every post on the subject, but I don't recall anyone straight up claiming the Templars were unequivocably brainwashed. Not saying it hasn't happened, but it's definitely not a majority opinion. For the most part they were led astray by leadership that was insane or stupid.