How do you tell your friend that you disagree with them without hurting their feelings?

I understand that we do not want to hurt our freind's feelings. When faced with a disagreement its best to put it forward in a mild manner. Such that you show you respect their thoughts but at the same time you disagree with them. It would also be good if you don't make it sound like you are right even if that may be the case

I believe starting with letting them know that you understand their point, and keep it on their point not them. Next I would ask them questions about their point and or ask them if they have considered... and offer an alternative view.

I would say that I understand where they are coming from, and that I will respect them for their opinion and that I do not agree with them on that matter.

This is actually kind of hard for me, because I have a thing about causing conflict. But I generally try to talk through the difference, explaining the rationale behind my opinion, and give my friend a chance to explain their side. Usually, the difference in opinion is because of a difference in background, so when you find out what is driving the other person, it's a lot easier to respect them and their opinion. You still might not agree, but if you approach it from a place of understanding, feelings usually stay unbruised.

By being polite and respectful and expressing your opinion stressing that it is your personal opinion and friends do not have to agree on everything.

I would say something like "hey I want you to know that I care about you but I don't agree with ..."

Acknowledge and try to understand how they are feeling, first. Then try explaining to them that you feel differently, but that their opinion is still valid nonetheless. Express that you understand where they are coming from and which parts of their opinion you might agree with and which you don't. Use sentences involving "I", for example say "I feel like this is the better option" instead of "You are wrong because". Assure your friend that you still cherish them despite not agreeing with them and explain to them that you can't always have the same opinion in a friendship and that that's okay. I'm sure they will understand!

In my experience, this is all about the wording and tone of voice. Rather than going out and saying that they're just wrong, say that you disagree. Be kind and calm about it. Show that you still respect their opinion and them as a person by not getting angry or rude to them.

Don't just outright say they're wrong, acknowledge them like maybe start with "I see where you're coming from but I think ...." and just stay respectful through it and don't make them feel dumb.

A true friend won't mind if you disagree with them. It mainly depends however on what it is. Try and avoid religion and politics unless you have both agreed to discuss it. Be respectful and tell them you disagree in a polite manner, ideally supported by facts.