That's a big list of characters, and several of them are incredibly minor characters with only a few speaking lines. I'll provide celebrities and some explanation to go along with the more central characters in Romeo and Juliet. Additionally, I'm not sure what exactly "relate" means in relation to the question. It could be asking which celebrity is like that character in real life (physically, emotionally, socially, etc.), or it could be asking which celebrity could effectively play that role. I'll use the second option.
Let's start with Juliet. She's going to be tough to find a celebrity for because of her age. Juliet is young, and most celebrities aren't huge celebrities by the age of 13. We know that she is 13 because Paris asks for Capulet's permission to marry her, and Capulet initially asks Paris to wait until she's older. You could go with Dafne Keen from the 2017 film Logan. She's 12 now, which puts her really close to Juliet's age. A better celebrity choice is going to be somebody that audiences will immediately "see" as somebody capable of falling in love, having an emotional roller coaster, and selling a suicide. Right now, the best choice is probably Jennifer Lawrence.
Romeo is a bit easier to cast. We don't know how old he is, but he is likely a little bit older than Juliet. He needs to be fairly good looking because audiences need to believe that Juliet could really fall in love with him at first sight. If I'm allowed to pick any celebrity from any decade, I would go with James Dean. That guy has "cool" oozing out of his skin. From current celebrities that are instantly recognizable and generally liked by audiences, I would go with Daniel Radcliffe or Josh Hutcherson. The former would probably be better because while Romeo needs to be good looking, he also needs to come across as sensitive and emotional as that is how we are introduced to him in the play; he's complaining about lost love.
Tybalt needs to be a celebrity who looks like a bad boy and can sell the "I'm angry all of the time" attitude. Wentworth Miller would be a good choice. He typically plays characters that are brooding and capable of snapping at any moment.
Lord and Lady Capulet could be played by Charlize Theron and Kiefer Sutherland. Both are old enough to be Juliet's parents, and both have enough acting depth to be loving one moment and overbearing and antagonistic the next.
Finally, the friar, I believe, needs to be played by someone older and skinny. That's just how I've always pictured him. Xander Berkeley would absolutely be my first pick. He's never been a headlining actor, but he is instantly recognizable. That's what you want for this character. Because he's always a supporting actor role, he's very good at selling the character that he's been given. He adapts well. Plus, his portrayal of Dr. Lamar from GATTACA is a similar type character to the friar.
Well, in a literal sense, almost no celebrities would relate to the smaller characters. If you're a celebrity, you're not going to have a life like, for example, the nurse. You would be famous, and living your own life, and the nurse is really living for Juliet.
That said, you could cast these pretty easily by looking at two things: 1) Their psychological characteristics 2) Their physical characteristics.
So, for Juliet, you'd want someone young, who can carry a scene on her own, and handle the attention of men, especially men older than she is, like Paris. This might be a Hillary Duff or an Anne Hathaway.
If you want real life situations, you'd have to go to tragedies or failed relationships.
For someone like Tybalt, you'd want someone who can carry off being an expert fencer, but also hot headed. That might someone young and lively, like Heath Ledger. He's played very physical roles. A Matt Damon would work too.
Do that throughout and you'll have your list.