“No offense” usually shows up right before the offense.

That phrase is a pre-emptive excuse, which means the speaker has already worked out that what follows will sting. It does not remove the sting, it asks you in advance not to react to it. Everybody recognises the move, which is why it tends to make the offence land harder rather than softer. If a sentence needs that cushion, the cushion is not the problem.

When you hear it coming out of your own mouth, reconsider the sentence behind it. Either say the thing without the disclaimer or do not say it. If somebody uses it on you, you are still allowed to be offended.