There is much dispute over the extent to which we can use the Iliad, for example, as historical evidence. People build careers by arguing that certain people, events, etc., existed/happened. Most of this, however, remains amongst academics. To the extent people are interested in Alexander who aren't historians, they simply trust whatever book they get out of the library or from Amazon (or just Wikipedia). The historical Socrates has concerned academics at least as long as the historical Jesus and many a career has been dedicated to arguing that Socrates' believed X not Y, that Plato can be trusted but not Xenophon, etc. Marija Gimbutas not only spent much of her career arguing over certain interpretations of evidence from prehistory entailed pre-historic Matriarchy and Goddess worship, something that is still accepted by many a modern Goddess worshipper and feminist but which fell out of favor among scholars of prehistory beginning in 1969. Much of Wicca came from the Egyptologist Margaret Murray's publications on the witch-trials which are now known to be riddled with errors from start to finish. There are scholars whose specialty concerns historical figures we know from almost nothing other than legend such as Hypatia or one or other of the pre-Socratics. Most of the time, the public is unaware such debates exist, nor would they care if they knew. In some cases (the few mentions of druids in the literature, the examples of Murray and Gimbutas I gave) certain people have been greatly concerned outside of academia, but to the extent they are interested in establishing that their beliefs about history can be defended they have in general tried as much as possible to find a common ground with historians (for example, most Wiccans who have practiced their religion for years no longer believe that Gardner was actually initiated into a coven that survived from the "burning times" but do argue, with a certain degree of accuracy, that their traditions and practices go back for centuries, in some cases over 2,000 years).
Read Cynthia Eller's The Myth of Matriarchal Prehistory: Why An Invented Past Will Not Give Women a Future for one counter-example (her book, like many a journal article and other academic publications, has argued expressly that no serious scholars of prehistory believe in matriarchal prehistory any more, but there are still those who believe outdated scholarship is correct). For another kind of counter-example, read Ronald Hutton's Blood and Mistletoe: The History of the Druids in Britain, which isn't really about the druids of history (he argues we can establish little to nothing about them), but rather how the desire to practice whatever it was/is that "druids" practiced has concerned certain members of the public for many centuries, and until fairly recently no small number of historians as well. In neither cases in which a religious-like motivation for a particular understanding of history or historical persons have those outside academia simply written off scholarship. Instead, they have altered their beliefs somewhat to incorporate scholarly consensus. So popular an author (and for many a serious Wiccan disdained as a sell-out wanting only to make cash off of teenage girls) as "Silver Ravenwolf" cites Hutton (professor of history and the foremost authority on Wiccan history as well as an expert on paganism, particularly Celtic and modern). For many a goddess worshipper, the former "historical" belief in a singular goddess in prehistory has become symbolic instead, and seen in various incarnations of goddesses from Demeter to Ishtar. This is because of repeated publications of the type "no scholars dispute X".
Only in the case of Jesus mythicism has their been both a widespread interest outside of academia a historical topic, a serious lack of studying before coming to conclusions, and a maintained belief that the 200+ years of study and thousands of specialists not been enough to support the conclusions reached in scholarship that isn't read but is dismissed.