It's also that (as has been proven by a large magnitude of people all over the world) for many people MLP has made a fairly positive impact on their lives. They made new friends or changed old habits for the better because the show encouraged them to. From that angle, it is not surprising that many people have a very strong emotional bond with the show because they attribute this personal change to the FiM, and they do so justly.
Now, when someone says that they don't like the show (in a hateful way or not), it seems quite understandable to me that such people could see such a statement as not just an attack on the show, but also on themselves, conciously or not. People who are less composed or who have a very strong emotional attachement to the show can get quite loud or even aggressive then. I also see it as possible that this can lead to completely neutral statements against the show, as OP pointed out, being misunderstood as negative or even trollish behaviour.
As Fifths pointed out, a major problem with Love and Tolerate is that it's not clearly defined what it actually means, and that no one is obliged to follow it. It's not a creed or a rule, it's just an idea, and not even a clearly defined one.
Personally, I like the phrase. While not actually coming from the show itself, it sums up its message quite well, IMO. What irritates me are people who flat out reject it, for reasons I completely do not understand. Then again, as has been mentioned already, different people interpret the phrase differently, since its meaning is not clearly defined and Bronydom as a whole has not reached a consensus on it.
Maybe we should do that.