Why tolerance is important? Because resistance is what happens within us if we do not exercise it.
Tolerance is the momentary conscious application of "allowing something to be without attacking it." For those of us who have to tolerate ideas or people we dislike, it is a constant momentary application (think of a bad Thanksgiving where we are merely "putting up with" a family member or their spouse) that keeps us consciously engaged so as not to be in a state of resistance.
Why does it matter that we are not in a state of resistance? Because the resistance is a "non-specific" energy that creates discord within the human body and crosses the boundaries of what specifically makes us uncomfortable and begins to affect all areas of our lives.
Tolerance of all possible ideas and things makes me more at peace than almost anything else ever has, even if the thing I put energy into tolerating are horrific to me. It makes my life more peaceful to tolerate the abhorrent than to allow resistance within the core of my being.
I for one, am not capable of living a peaceful and content life with resistance in my body ... and while some may argue that they are capable, I would still suggest it even easier to allow that which makes us uncomfortable and tolerate its presence rather than resisting it.
Tolerance doesn't mean we don't fight to change or influence that which is gnawing at our bones, of course we do. That is harmonious with integrity. But we do not have to be in a state of resistance for that.