Luffy's journey since the beginning of One Piece would not be possible without his crew members who have joined him over the years. Each Straw Hat member contributes something to the crew that helps Luffy get closer to his dream with each story arc. The Straw Hats have made clear on several occasions that they are willing to give up their lives if it means Luffy's dream of becoming Pirate King can still come true.
Looking back through the story, Luffy deserves every bit of the belief his crew members place in him and his dream. He has saved and changed each of their lives immensely. Before they met Luffy, most of the Straw Hats were in hopeless situations, living lives they didn't want. Some of them might even be dead by now if not for how strong Luffy's love for his friends is.
When Luffy met Zoro in One Piece, the latter was tied to a cross awaiting imminent execution. Rumors portrayed Zoro as an evil pirate hunter, but Luffy learned that wasn't true, deciding to free Zoro and get him to join his pirate crew. Zoro went from being a captive pirate hunter to a pirate himself, becoming Luffy's first crew member. Joining Luffy also meant having the opportunity to honor a promise he made by becoming the greatest swordsman in the world.
Nami seemed like any normal girl when she first met Luffy, except that she was trying to collect 100,000,000 berries. When Luffy initially asked her to join his crew, she refused, stating that she hated pirates. Nami's claim and wanting to collect that sum of money didn't seem like anything to be taken seriously at first. However, the Straw Hats later found out that Nami had a very tragic reason to hate pirates and was desperate for so much money.
Cocoyasi Village, Nami's home, had been under the rule of the tyrannical Fish-Man pirate Arlong, who demanded that the citizens pay him for their lives. He wanted 50,000 berries for kids and 100,000 for adults. Nami's adoptive mother, Bell-mére, sacrificed her life in exchange for Arlong letting Nami and her sister live free lives. Bell-mére could only afford to either pay for her daughters' lives, or her own with the 100,000 berries she had. Arlong even killed Bell-mére in front of the two girls.
Going even further, Arlong went against his word and decided to force Nami to work for him. She made a deal with the tyrant to buy back the village, hence the 100,000,000 berries she was trying to collect. When Nami tearfully begged Luffy to help her, he immediately said he would. Luffy wasn't even aware of the specifics of Nami's situation -- he just knew his friend needed his help, so he gave it.
Luffy defeated Arlong, saving Nami and Cocoyasi Village. She might have never been freed from Arlong's tyranny without his help. She decided to join his crew and help him on his journey as the Straw Hats' navigator. Nami's dream in One Piece is to use her cartography skills to draw a map of the entire world. Traveling as a member of the Straw Hats makes this possible.
When Sanji was blackmailed by his father, Vinsmoke Judge, to marry into Big Mom's family, he initially refused to accept the Straw Hats' help. As a child, Sanji was constantly abused by his father and siblings. He inevitably reached a breaking point and ran away, which led him to eventually joining Luffy's crew years later.
Judge had exploding handcuffs placed on Sanji to keep him from escaping Whole Cake Island. Moreover, he threatened to have Zeff killed, knowing how much he means to Sanji. This forced Sanji to attack Luffy and act as if he wanted nothing do with the Straw Hats, even claiming he'd rather embrace his royal heritage than go back to Luffy's inferior pirate crew. Luffy didn't believe his act and refused to leave.
Sanji eventually gave in to Luffy's persistence and admitted he wanted to go back to the Straw Hats. Luffy was ready and willing to do whatever it took to make that happen, and he and his friends fought a long, harrowing battle against Big Mom and her subordinates. They managed to escape Whole Cake Island with their lives, saving Sanji from being trapped in a nightmare situation.
When Robin was first introduced in One Piece, she was working under the villainous pirate Crocodile. It was later revealed she had been on the run for 20 years. The World Government brainwashed people into believing she was a threat to the world as the last survivor of Ohara. Robin spent years seeking refuge from different people, but they all tried to turn her in to the marines or kill her themselves.
Robin officially joined the Straw Hats after the Alabasta arc. Her dream is to discover the true history of the world by finding the Rio Poneglyphs. However, the World Government eventually caught up to her and the Straw Hats, which prompted her decision to leave the crew and cooperate with CP9 to protect her friends. The World Government was planning to have her killed but Robin didn't care; she was willing to sacrifice her life if it meant the Straw Hats could go free.
Naturally, the Straw Hats refused to accept Robin sacrificing herself and followed her and CP9 to Enies Lobby, where multiple battles took place. Just when Robin had given up on living, telling herself it's alright if it's to protect her friends, Luffy urged her to admit she wanted to live. The Straw Hats fought the members of CP9 to save Robin and won. She rejoined the crew and continued pursuing her dream.
Luffy has impacted the lives of Usopp, Chopper, Franky, Brook and Jimbei in similar ways to the other crew members. He gave them all hope when they had resigned themselves to hopeless fates. He saved their lives and gave them a chance to pursue their dreams the way he's pursing his. If they hadn't met Luffy, each Straw Hat member would either be dead or living a horrible life they didn't want.
The Straw Hats prioritizing Luffy's dream over their own makes perfect sense in retrospect. He changed their fates and made it possible for them to achieve their own dreams while helping make his own come true. It's not unusual at all that they're willing to give up their lives for him. The One Piece protagonist has done more than enough to earn that level of loyalty.
