Giving blood to a kaafir who is not hostile towards Islam and who is not in a state of war with us

Shaykh Ibn Baaz (may Allaah have mercy on him) was asked about that and he
said: 

“I do not know of any reason not to do that, because Allaah says in His Book
(interpretation of the meaning): 

“Allaah does not forbid you to deal justly and kindly with those who
fought not against you on account of religion nor drove you out of your
homes”

[al-Mumtahanah 60:8]

So Allaah tells us that He does not
forbid us to deal justly and kindly with those kaafirs who are not fighting
us and who have not driven us out of our homes, or with those who are in
urgent need of help. The mother of Asmaa’ bint Abi Bakr al-Siddeeq (may
Allaah be pleased with her) came to her daughter in Madeenah, at the time of
the peace treaty between the Prophet (peace and blessings of Allaah be
upon him) and the people of Makkah, and she was still a kaafir, to ask her
to uphold the ties of kinship. Asmaa’ consulted the Prophet (peace and
blessings of Allaah be upon him) and he told her to uphold the ties of
kinship, saying, “Uphold the ties of kinship with your mother even though
she is a kaafir.” 

If a kaafir who has a peace treaty with the Muslims or is under the
protection of the Muslims, and is not hostile towards Islam and is not in a
state of war with us is in urgent need, then there is nothing wrong with
giving blood to him. You will be rewarded for that, because there is nothing
wrong with you helping one who is in urgent need of charity or help. 

From Kitaab Fataawa Noor ‘ala al-Darb, vol. 1, p. 376 

Based on the above, if the kaafir is
hostile or in a state of war with the Muslims, then it is not permissible to
give him blood, because by doing so you are helping him in his aggression
against the Muslims. This is a very serious matter. We ask Allaah to keep us
safe and sound.