All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There are no religious impediments in marrying this man who had a kidney transplant. Indeed, we have seen many people who underwent such a transplant and lived for long and had children.
Therefore, if this man is religious and has a good moral conduct, then you may try to convince your parents to accept your marriage to him.
First of all, you should seek the help of Allaah [by supplicating Him] and then the help of whomever you think could influence your parents. If they accept, all perfect praise be to Allaah, but if they insist on refusing, you should obey them.
Indeed, the parents are usually affectionate [towards their children] and this makes them look to what is more beneficial for their daughter.
Furthermore, it is not an obligation on you to marry this specific man, and Allaah may bless you with a better husband due to your obedience, kindness and dutifulness to your parents.
Allaah Knows best.