It's not only English speakers that have a taboo against naming their babies Jesus. It is extremely rare in other European countries as well; Danes, Germans, Russians, etc don't use the name either. It comes from the commandment that directs Christians not to use the Lord's name in vain. A more accurate question is why is it not taboo in most Spanish speaking countries?

It started during the Moorish occupation of Spain. Spanish Christians began naming their sons Jesus as a reaction to Moors naming their sons Mohammed. It was an act of defiance, and publicly identified them as Christians. The practice continued long after the Moors left Spain, and many of the countries Spain occupied/conquered/founded use it as a name as well. It is common in Central and South America as well as the Philippines.

Source: The book 'Moorish Spain' by Richard Fletcher.

I also heard that it is Joshua. Fair enough, but football players don't yell "Thank you, Joshua!" People don't say "Joshua Saves".

To make things clear, Jesus and Joshua aren't the same name. They have the same ultimate origin, but a different path to English. "Joshua" is from the Hebrew "Yehoshu'a", filtered through various languages (Latin). "Jesus" is from the Greek Ἰησοῦς, which is from the Hebrew/Aramaic "Yeshu'a". It gets confusing because Greek uses Ἰησοῦς for both the Hebrew Yehoshu'a and Yeshu'a because those two names are related, but they're not the same name.

It is also a relatively common name in Arabic cultures, "Issa", even among Muslims.

In Spain proper, is Jesús a popular boys name?

I don't believe it is, correct me if I am wrong. So the question might be rephrased as 'why did the name become popular in Latin America?'

Edit: So Jesús is a popular name in Spain but no Spaniards named thusly have achieved fame outside the Kingdom, and we are still no closer to answering the question raised by OP.