Avoid phrases such as "Now don't get offended by what I'm about to say, but -" or even "Now don't take this the wrong way, but -". These types of phrases may seem on the surface level to be polite phrases to soften the blow of what you're about to say, but in actuality these phrases often have the opposite effect and can make what you're saying sound more upsetting and/or offensive instead of less upsetting and/or offensive.

First and foremost, these phrases signal to your conversational partner that something potentially upsetting and/or offensive is coming, and rather than that softening what they hear, this often puts people on guard, which can lead them to feel / react more defensively.

It can also make some people wonder if they should be upset or offended by what you're saying when you lead with these phrases, but it might not have occurred to them that your words could be taken offensively if you had just not lead with those phrases.

Second of all, phrases like this shift the blame from the speaker to the listener. When you lead with any of these phrases, it's subtly blaming the listener for any way they might be hurt or upset by your words, when the responsibility should actually be on you to speak with tact and not say hurtful things to other people.

Imagine telling someone "Now, don't be hurt by what I'm about to do!" and then punching them in the face. If you can understand why it's unfair to tell someone to not be hurt by being punched in the face, rather than just not punching them in the face, then hopefully you can understand why it's unfair to tell the listener to just not be hurt / upset / offended by your words.

Telling people to just not feel upset or hurt by what you're saying to them can come across as dismissive, or even manipulative. Their feelings are their own and not for you to command.

And finally, phrases like this often come across as patronizing and condescending. Phrases like this can come across as if you think your conversational partner is overly sensitive, irrational, and/or incapable of handling honest conversation, which can definitely make these phrases come across as patronizing and condescending.

So instead of just telling your conversational partner to not be upset or offended by what you're going to say, instead learn to phrase what you want to say tactfully, or ask yourself if it's actually necessary to say in the first place. If you want to say something that could be wrongly interpreted, it's more concise and effective to just clarify that you don't mean it that way rather than just telling the other person to not take it that way.

For example:

Say your friend knows you're going for a solo hike this weekend and asks if she can join. Instead of saying "Don't take this the wrong way, but I'd rather go alone." Try something like "I enjoy your company and love spending time with you, but it's important for me to have my alone time out in nature." In this example, since the way your friend could take you preferring to hiking alone "the wrong way" to mean that you don't want to spend time with them, it would actually be clearer and more effective to just say that you do actually enjoy spending time with them and that's not the problem.

You can also try replacing "don't get offended" and/or "don't take this the wrong way" with:

“I’m saying this with the best intentions”

“I mean this in a constructive way”

"I mean this in the best way possible"

These are phrases that signal good intentions on your end rather than placing responsibility on the other person.