Are all hadiths disputed in terms of their authentication and weakening, or are there hadiths whose authenticity is agreed upon?

Not all hadiths are disputed; many are agreed upon as authentic, including the mutawatir (recurrently transmitted) ones. Scholars have agreed to accept what is contained in Sahih al-Bukhari and Sahih Muslim. The judgment of a hadith as authentic or weak is a matter of ijtihad (independent reasoning), and scholars may differ on the authenticity of a hadith due to their differing views on the fulfillment of authenticity conditions or on the necessity of some of them. If a hadith is said to be authentic, it does not mean it is definitively established. The differences among narrators and the varying judgments on hadiths stem from many reasons. The science of hadith and its rules are among the greatest sciences, and the methodology followed in verifying the authenticity of hadiths is among the most precise methodologies for transmitting news.