I’ve been thinking about dyeing my hair a different color for a long time, but my family is completely against it. They say things like, ‘You look better the way you are’ and ‘You’ll ruin it if you dye it.’ But I really want to make a change inside. What would you do in a situation like this? Do you think it would be bad if I just did it without asking for permission?
I was in a similar situation once. While preparing for university, I wanted to dye my hair blue, and my mom reacted quite strongly. But I really
If you want to dye your hair, first be careful not to use a lightener. People generally fear that lighteners cause more damage. Get a temporary dye in a few darker shades. This way, there won’t be a huge change, and they won’t get too mixed up.
I’m telling you, no one should take it personally, but why don’t you think about why your family is against it? Are you pushing so hard just for the sake of stubbornness or change? Hair will eventually go back to its old state anyway, why don’t you try sitting down and talking a bit more 
To be honest, hair dye doesn’t directly damage your hair, but if you don’t take care of it, you might experience breakage and dullness. If you tell your family that you’re looking into plant-based dyes, maybe you can convince them a bit. Also, consult a hairdresser first; choosing the right color for your hair type is important.
Let me add that I actually haven’t completely talked to my family. I only mentioned it a couple of times in passing, and they immediately objected. I didn’t sit down and explain it to them seriously, but it seems like they’re not going to accept it anyway 
I swear, the main issue here is ‘your body, your decision.’ I think dyeing your hair is a matter of freedom. You shouldn’t have to seek approval, but it would still be good to communicate openly to strengthen your connection. 
Talk, talk if you can’t find a way, you know there’s temporary spray paint, right? It stays on your head for two or three days, then it washes off. Give it a try, maybe when they see it they’ll say ‘let’s make it permanent’, or at least you’ll get a reaction.