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first-and-foremost a problem at the receiving end (given they are delivered respectfully)The problem is that respect has many layers. What the speaker considers respectful may not at all be experienced as respect by the listener.
I think we all need to work on both sides: we need to do a better job of listening to truth instead of rejecting it; and we also need to do a better job of calibrating how we express the truth so that our expression can have good effects rather than harmful ones.
In my experience, people who see themselves as deliverers of objective truth and see other people as deficient in truth-hearing capacity (I'd include myself in this group btw) do tend to have an oversimplified view of this, and yes, do tend to be unconscious of the effects they're producing, which they mostly ascribe to inadequacy in their audience.
Don't get me wrong—I'm not suggesting that anyone reduce their passion for truth. I'm saying it's one axis and there are other axes that are orthogonal to that one—for example the relational axis. Where you're located on those other axes also matters. If you occupy a point of high passion on the objectivity/truth axis and low awareness on the relational axis, it becomes easy to cause both others and oneself a lot of pain. You can think of the truth—especially uncomfortable truth—as a power tool. Wielding it skillfully is important.
The solution is to maintain one's high passion for objectivity and truth while at the same time taking up the work of advancing where one stands on the other axes.