I know that there are very different standards of evaluating the authenticity of hadiths in both sects. However, when there are no contradictions between a certain hadith and the sect's criteria for an authentic hadith, do Sunni/Shia scholars tend to accept the hadiths collected by individuals from the other sect?
Yes, Shia and Sunni scholars do study and evaluate the hadiths collected by the other sect, although they may approach them from different perspectives.
Shia scholars generally give greater weight to hadiths narrated by members of the Prophet Muhammad's family (the Ahlulbayt), while Sunni scholars tend to rely more on hadiths narrated by the Prophet's companions (the Sahaba). Nonetheless, Shia and Sunni scholars do examine and critique each other's hadith collections, and they may also rely on shared collections of hadiths that are considered authoritative by both sects, such as the collections of Bukhari and Muslim.
It is important to note that the interpretation of hadiths can vary widely depending on the school of thought and the individual scholar, and disagreements over the authenticity and meaning of specific hadiths have been a source of ongoing debate and controversy between Shia and Sunni scholars for centuries.