This is a good question!

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I think to start it's helpful to sort between levels of significance or consequence regarding the historical claims being evaluated.

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For example, there's a difference between stories or anecdotes that are commonly believed and often repeated because they're entertaining or compelling narratives but that aren't important to any contemporary ideological, political, religious or cultural system and interpretations of history that are frequently cited or used in contemporary political and ideological contexts.

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Stories that are commonly believed to be true may in fact be known by historians to be questionably sourced (or outright false) but it may not be particularly urgent or important for ordinary people to correct themselves. Say, for example, the often-told story that audiences in Paris ran in terror from an early film showing a train coming towards the camera. Frankly, early in my career as a historian, I myself assumed that story was true, until I read a number of film historians saying that there was no evidence that it ever happened. It's the kind of story that we assume is true in part because it makes us feel superior (ho-ho! we are smarter than the dumb people in the past) but also because it lets us express some deeper continuing anxiety we have about film and its impact on real life. I don't know that it does any harm to believe this story is true--though I think most historians wish that people would quickly correct their stubborn attachment to such false stories once they hear otherwise.

But for more consequential matters, I think there's no easy alternative to doing a bit of reading any time that it seems as if historical claims are important to contemporary arguments, policies or ideologies. Perhaps even before reading specifically what historians have had to say, a member of the general public can learn some diagnostic signs of whether a particular claim is contested even among historians. Titles of books and articles published by scholarly historians can sometimes be a clue ("A New Interpretation of X", "New Approaches to Y"), as can the sheer volume of scholarly activity around a particular topic or argument. I would equally argue that if a quick search of titles, publications or links around a particular argument or interpretation shows a sharp divergence between scholarly historians on one side and people who are not historians or academics on the other, that would be an indicator in and of itself of "wide agreement", before ever reading the content.

For someone who honestly wants to know whether historians generally or commonly agree on a point that is important to contemporary policies or politics, a natural starting place might be the major college-level textbook in the relevant field. Most historians who write textbooks intended for use in survey courses will describe both what is commonly agreed upon, what is not commonly agreed upon, and the historiographical background behind any consensus (e.g., how historians came to accept a particular view, and whether they ever thought otherwise). Historians of very divergent temperaments and political perspectives nevertheless often share a view of what makes for good and bad evidentiary claims and often are very responsible in their summaries of past historical thinking on a given subject. (Not the least because such a summary is often the justification for one's own work: that you are questioning, revising or adding to existing thinking.) Many textbooks will also be helpful in providing a short list of additional suggested readings, if additional confirmation or information is sought. There are also a number of good books that can be used as textbooks but have other possible uses--the Oxford University Press Very Short Introductions series is one great example. Any book that bills itself as an introduction or overview can suit. In a pinch, except on certain highly controversial subjects, Wikipedia entries are often reasonably good at identifying existing consensus views among historians.

This approach will be most helpful when it is a specific issue or event in question. If you want to know, for example, whether historians generally agree that slavery was the main issue precipitating the American Civil War, any good college-level textbook or general work on the Civil War is going to quickly establish that there is almost universal consensus among scholarly historians that it was in fact the main issue. On more abstract, general or sweeping interpretations, the challenge facing a member of the general public is a good deal more difficult. Say, for example, "Is there consensus about what led to the relative rise of Western Europe within the world economy after 1450?" is going to be a tough thing to sort out easily for a non-historian who simply wants to know what the state of play within historical scholarship is. I think however that it might become quickly apparent simply on a search that there is not a single strong consensus, even if identifying the various contending views might take more guidance.