Should I be diplomatic at my workplace?

Yes
You should be diplomatic at your place of work, being diplomatic is of immeasurable value. It shows that you always find the right manner in which you deliver information to your colleagues, subordinates and superiors. It shows you have the ability to understand feelings, ideas and opinions of others.

Diplomacy is a skill set that should be mastered by all professionals irrespective of their rank in the workplace, because it strengthens the relationship in a workplace and it helps decrease the level of negative energy impact upon receiving unpleasant or unfavourable feedback.

I would say it is wise to be diplomatic wherever you are, even if talking to a young child! Yes, you will be more popular and probably more effective a worker if you are diplomatic. How does it help anyone's work situation to feel embarrassed or angry about what is said to them?

I imagine there is something you feel critical about but are unsure what to do about this. If you are in a position of seniority and responsible for the output of that person, then you must correct any short-comings in their work.

YOu can do this without being offensive. If the person is a peer or a senior, best hold your tongue and concentrate on making sure your own work is of good standard.