Sensitivity can really strengthen a sermon.  If it is overdone it can also neutralize a sermon, but well-placed and well-worded sensitivity is well worth the extra thought it takes.  If the text was originally targeted at one specific type of person (such as the early chapters of Proverbs targeted at young males), perhaps a careful comment or two can open up its relevance to a wider audience.  Or in your illustrations and applications, perhaps another one is needed to include a group that may feel excluded.  Or when the subject can feel sensitive to some, a careful acknowledgement of that is well worth considering.  For example:

Singles.  A lot of biblical stories and teaching relates to marriage, either human or the relational image of God and His people.  For some singles in the church, this can be hard to take.  Sensitivity to their feelings can really help.

Childless.  It is natural and easy to relate stories of your own children, but for some in the church this can be painful since they remain childless.  Be especially careful in biblical stories where God has “closed the womb” as a form of discipline.

Women.  It is definitely worth being sensitive to the existence, worth and ability of women.  Make sure your illustrations don’t always default to male imagery, male characters, and male thinking patterns.  As ever, too much is generally not appreciated by men or women, but deliberate well-placed sensitivity is well worth the effort.

The elderly.  High energy practical applications for hectic families and workplace interactions can easily miss the elderly who no longer have a full nest, a full work schedule or even a full tank of energy.

The unemployed.  In our desire to be relevant to the majority, we can easily apply the sermon in respect to work life.  There may be some wrestling with the reality of unemployment and the many feelings that come with that.  They probably don’t want to be put in the spotlight, but will sense your sensitivity.

So five groups of people that can easily feel left out or even hurt by insensitivity from the pulpit.  Any other groups we should be aware of in our sermon preparation?  A well-placed and well-worded comment here and there, an extra illustration from daily life, and our sermons will be strengthened by sensitivity.