Whether we like it or not, in every stage of our lives we will always come across at least one person that is so stubborn, it seems like they are stuck in their own realm. But from my experience, there are 3 different types of stubborn people out there in society, so let me make your life easier by giving you my tips which I can say confidently, has helped me a lot.
The first, as I've mentioned above, are those that have already "created their own world". What I mean specifically by this is that these are the type of people who aren't willing to expand, grow and improvise on themselves as their minds are already fixated and hardwired to their own morals and values. One example of this from my experience is the elderly people I have encountered who seemed to have done the same routine for so many decades that introducing something new to them is like searching for a needle in a haystack. One of the best ways to handle this situation if you were to convince them or persuade them of something is to list more advantages than the disadvantages of something in particular, then say the magic phrase; "its completely up to you". Why do you ask? this way you seem less like a salesman who tries to force their products on a customer which will put less pressure on them. the whole idea is to make them feel as though they are losing or missing out on a great opportunity.
The second type of stubborn people which I guarantee you will come across or have already may have come across is "Mr/Mrs. Right". These are the ones that will always deny being in the wrong no matter how right you are or how hard you try to get your points across. This suggests that they lack the ability to understand a situation from another's perspective or point of view. My advice to all of you is to save your time and energy by moving on and let thim "win". this way it makes them look stupid and possibly realize their mistake if they come back to their senses. proving them wrong will only do the opposite.
Finally, we have the ones that are strongly opinionated which may not necessarily be classified as stubborn. But they are those that are very quick to disagree just to make themselves seem intellectual. In my case in most of the situations, i'd reply or agree in a very sarcastic way that it makes them look dumb. Funny thing is, they never realize this because their ego is too high.
To summarize, take it as a pinch of salt or a form of entertainment when you come across these types of people and never take things seriously because that is their nature and will always be.