Most "truth" is relative anyway.
And the one who wants connection seems to want the other to connect on THEIR terms.
Here is what I think the OP is saying. You have a friend who tells you that you are too sensitive and cannot hear their "truth" because it comes across as a criticism. But you really want that person to connect with you emotionally and in a way that facilitates warmth and kindness in the relationship, and then hearing the other's "truth" would be much more palatable. I hope I got that right.
Here is the connection. It's not a "versus" thing, but rather building the relationship to the point that you can each withstand the "truth" from the other. And you can't expect the other to hear the song of your heart and learn the words of your song unless you listen for their song and learn their words and sing along first. That goes for both people in the relationship. Both need to initiate the work it takes to really listen for what makes the other person tick, understand it, and then attend to their needs - especially their emotional needs. This is called attunement. Both must tune in to the other, and not just expect to be tuned into without reciprocating. The only relationship that is all about you, is with a therapist. Otherwise, it's about tuning in to the other person.
When tuning into someone else becomes a natural part of the relationship, then it facilitates attachment. The other person then seeks you out and attaches to you because you are tuned into them and they need to feel understood and loved.
Once you have a solid attunement/attachment relationship, then you will be more willing to hear their "truth", and they will be more willing to hear yours. The relationship will be able to withstand a little constructive truth. The person speaking their truth must do so with the other person's best interest in mind and it must be selfless (no gain for themselves) and in love. And if the relationship is good, then the person hearing the others' truth will be able to accept it and consider how it could be true for them - again, it is an opportunity to attune to them, understand how they came to that "truth" and honestly evaluating whether it is indeed, true, or if it's something that needs to be clarified so they will understand your truth.
How does this apply in a sermon? How much do you trust your pastor? Are you open to feedback, if he is directing it at you? If he's not directing it at you, then take what he says, go home and study the issue in the Bible and see how true it is. And if it's not so much something that can be studied, then maybe he said something that struck a chord in you and you know deep down to be true, even if it was communicated in a way that you don't like.
How does it apply to work? In the same way as I described above, only within company policies and practices. If a colleague has an issue with you, listen for understanding where your colleague is coming from, validate their experience, introspect and be honest with yourself about whether it's true. If it is, you can do something about it; if it isn't, then you can just let it go as maybe their issue rather than yours.
How does it apply at home? Always seek to understand your spouse. Clarify issues, be honest with yourself and open/vulnerable with your spouse, and think about the things your spouse feeds back to you. How you say something will matter greatly here, as it must always be done in love - and love isn't always gentle. Sometimes what they say will hurt us - especially if there is a little truth to it. Validate where they are coming from, validate their experience. It does not mean you have to agree. But again, introspect and examine your heart. Ask the Spirit to examine your heart and tell you the truth about it. Then listen for the answer, and brace yourself for his truth. Be prepared to be humble before your spouse if you need to be.
Hopefully that helped or made a little sense.