Do not waste water, even if you perform your ablution on the banks of an abundantly-flowing river
Is this hadith authentic? if it is not authentic, should Muslims still act on it?
This hadith appears in the collection of Ibn Majah, under the chapter "Concerning Moderation In Ablution And Avoiding Extravagance." This particular chain is classed "weak." link
However, this hadith appears in other collections. In particular, the version in Musnad Ahmad is graded Sahih by Ahmad Shakir. Al-Albani also collected this hadith in his Silsilah As-Sahihah (#3292) and graded it Hasan. The main disagreement appears to be over one of the narrators in the chain: Abdullah b. Lahi'ah, whose ability to narrate is differed upon. Another muhaddith Ala'addin Mughltai said the chain is weak but in meaning the hadith is Sahih.
In any case, the general principle of avoiding extravagance is established by strong ahadith, and the jurists say that in such a case acting on more specific but weak ahadith that point to virtue is permissible. Even if one were to not act on the exact words of this hadith there are plenty of other hadith (look at the hadith above and below this one in Sunan Ibn Majah) that document the little water with which the Prophet (saws) made wudu, his (saws) general warnings against extravagance, and his command to us to make wudu like he made wudu.
The most correct rule on weak ahadith is to judge both the chain of narrators, the Isnaad as well as the content, the Matn. If in as is the case here the chain is weak but the content is strong and not in any disagreement with other ahadith or the Qur-aan then we may retain the hadith as long as we are not using such hadith to implement laws such as inheritance, divorce etc.