According to the Hanbali madhab, camel meat is a nullifier of wudu and hence it is obligatory to repeat wudu after eating it. Their evidence is the hadith:
أن رجلا سأل رسول الله صلى الله عليه وسلم أأتوضأ من لحوم الغنم قال إن شئت فتوضأ وإن شئت فلا توضأ قال أتوضأ من لحوم الإبل قال نعم فتوضأ من لحوم الإبل
A man asked the Messenger of Allah ﷺ whether he should perform ablution after (eating) mutton. He (the Prophet) said: Perform ablution if you so desire, and if you do not wish, do not perform it. He (again) asked: Should I perform ablution (after eating) camel's flesh? He said: Yes, perform ablution (after eating) camel's flesh.
— Sahih Muslim
According to the majority (Hanafi, Maliki, Shafi'i), camel meat is not a nullifier of wudu and it is not obligatory to repeat wudu after eating it. Instead they interpret the above hadith to be meant in the sense that it is mustahab to do wudu after eating camel; the reason for the recommendation could be because the meat has an unpleasant smell which would be washed away.
Their evidence includes:
كان آخر الأمرين من رسول الله صلى الله عليه وسلم ترك الوضوء مما مسته النار
The last practice of the Messenger of Allah (ﷺ) was that he did not perform ablution after taking anything that was cooked with the help of fire.
— Sunan Abu Daud
Camel meat is included in what is cooked with fire. Also, if the first hadith was based on obligation rather than recommendation, this one would indicate its abrogation as it narrates the final practice of the Prophet.
أن رسول الله صلى الله عليه وسلم قال:الوضوء مما يخرج وليس مما يدخل
The Messenger of Allah ﷺ said: Wudu is done for that which is excreted, not for what enters [the body]
— Sunan al-Daraqutni & al-Bayhaqi
Similar to the above, this indicates that eating anything does not nullify wudu.
It is claimed to be the madhab of a group of the prominent sahaba including Abu Bakr, Umar, Uthman, Ali, Ibn Masud and Ibn Abbas.
فاختلف العلماء في أكل لحوم الجزور وذهب الاكثرون إلى أنه لاينقض الوضوء ممن ذهب إليه الخلفاء الأربعة الراشدون أبو بكر وعمر وعثمان وعلي وبن مسعود وابي بن كعب وابن عباس وأبو الدرداء وأبو طلحة وعامر بن ربيعة وأبو أمامة وجماهير التابعين ومالك وأبو حنيفة والشافعي وأصحابهم
The Ulema differed about eating the flesh of Camel. The madhab of most is that it does not nullify wudu and this is the view of the four caliphs, Abu Bakr, Umar, Uthman, Ali, Ibn Masud, Ubay ibn Ka'b, Ibn Abbas, Abu Darda, Abu Talha, Amir bin Rabi'a, Abu Umamah and the majority of the Tabi'een and Malik, Abu Hanifa and Shafi and of their companions.
— Sharah Sahih Muslim - Nawawi
It is supported by analogy: Camel is like all other foods, it is agreed upon that it is not unclean (if it was it would not be permitted to eat it) and it does not have anything common with the things that break wudu.