The BoS have been acting a certain way for three games now. Beth comes along, and suddenly they're acting entirely different.
Not really. The Midwestern Brotherhood (what I assume you mean by the third game) didn't really act the same way the West Coast Brotherhood did. But just looking at the first two games, and then the third game, I don't think there is the marked changed that some people seem to think there is.
The original Brotherhood had their attitude, and obviously a lot of the "rank and file" Brotherhood were (and are) just fine with that attitude. This attitude is still present in Fallout 3. Lyons isn't very traditional, but some of his men both are and were. The most extreme example of this of course are the Outcasts, which some people like to consider the "true brotherhood", but you can still see it in some of the loyal Brothers... Paladin Bael, for example, among others.
But there are - as I've pointed out - hints in the first two games that this attitude was not, in fact, universal. But, as a relatively isolated, close-knit, tradition-bound organization it would be impossible for enough of the "radicals" to get any real power. But when conservative, tradition-bound people are confronted with a threat to their ways, they tend to react by stagnating even further. This results in the situation John Maxson had to deal with: A council that was so divided on many issues, paralyzed by an inability to reach a consensus on anything.
Now you have the East Coast Brotherhood, being somewhat removed from the direct oversight of the Lost Hills Elders, forced to make a certain amount of autonomous decisions. Lyons, while initially a conservative, traditional Brotherhood member, gets influenced by what he experiences in the east. He begins to exceed the scope of his original mission, and this causes a commotion among the Lost Hills elders. On one side, you would have those that felt, like Casdin, that Lyons was betraying the Brotherhood. On the other hand, you probably would have those who were more sympathetic to Lyons ideas. Once again, the council is deadlocked - the "radicals" refuse to condemn Lyons, but the traditionalists refuse to support him. End result, a compromise that really pleases no one: A hands off, "We'll see what happens, but not provide any further aid" policy.
Now I grant you some of this is speculation on my part, since we hardly have, for example, minutes of the Lost Hills Elders meetings on the issue. But this fits with how the Brotherhood seemed to me in the first games. Or to put it another way, I don't see the East Coast brotherhood as "suddenly acting entirely different"... I see it, in a sense, as a magnification, or perhaps culmination, of a division that has existed in the Brotherhood since the first game.