There are a few questions in this post, so I'll go through them one by one in the most convenient order.

a lot of historical figures would have hidden the fact they were LGBT, right?

Absolutely. I'd say this is pretty common knowledge, but in case it needs clarification, there have been countless societies in the past where LGBT people would have had every reason to keep quiet about their true orientation and gender out of fear of persecution and other drastic penalties.

the cultural meaning of behaviors that I would regard as obviously gendered or romantic must change across places and over time [...] so how do historians puzzle it out? [...] Is there a standard for deciding?

You've touched on the crux of the question in your own post here. Your original question asks whether someone was "really LGBT", but this is taking every historical figure ever considered out of their original context and deciding which modern "LGBT-or-not" box to shove them in. As an example, in Ancient Rome, for a man to bugger another man was not considered a homosexual act for the penetrator - for the man being penetrated, however, the act indicated a homosexual leaning. Are either of the men in this scenario "really LGBT"? In the context of the time, yes, one of them is. Is there a standard for deciding? Absolutely. For the Romans, it's quite straightforward - being penetrated is homosexual, penetrating is not.

Asking whether they are "really LGBT" in the eyes of modern historians is an entirely different question, and involves ripping the situation completely out of context. Is there a standard for deciding whether someone is LGBT in modern times? It depends who you talk to. As you touched on in your question, the standard for what is a romantic or sexual (and straight or LGBT) interaction varies massively worldwide. As such, you could say that there are many standards for deciding, varying according to each individual historian's beliefs. However, if you're asking whether there is a "The Standard", a codified set of criteria to decide whether someone in the past was LGBT, the answer is no. There is no gay-o-meter that measures up our ancestors.

How do they know what evidence means?

This is partly linked towards the first question, and I want to be completely clear here to prevent ambiguity. If you are asking how historians know whether a piece of evidence indicates that someone was LGBT by modern standards, the answer is that they don't. See the previous paragraph on how these standards either exist so idiosyncratically that they aren't relevant or don't exist at all.

If you're asking how historians know whether evidence indicates that someone would have been considered homosexual in the context of their own time, the answer is much clearer. Most of the time, we know because someone wrote an accusation of some kind that accused them of exactly this behavior. To return to the example of Ancient Rome, we have many examples of politicians of the time accusing one another of having received penetration from their political superiors to further their own goals - "gay for pay", if you like. For the vast majority of recorded human history, there were no slander laws, so people in many societies flung accusations of such behavior around left and right.

Figuring out whether these accusations were true isn't always easy. Sometimes, we have to admit that we just don't know, though it is likely that many of these accusations held no water whatsoever simply because of their sheer and grotesque volume. At a certain point, it all gets philosophical, so we have to cling to the facts. A man was executed for homosexuality. Asking "was he actually gay" is a pop history question rather than a serious historical enquiry. Asking "did he ever engage in acts that were considered homosexual at the time" is really hard to answer. Perhaps a witness walked in on him performing such an act, but was the witness lying? We have no way of knowing. In the end, all we can readily conclude was that he was executed, and probably for reasons of homosexual conduct - at least, that is the recorded reason.

Do they just assume everyone is cisgender and straight unless proven otherwise?

No. There are plenty of historical figures who showed no obvious indicators of their gender or sexuality in the evidence available to us. If an individual from the past never indicated any particular direction on these issues, they are not assumed to have been considered straight or otherwise in the context of their time, because it is not relevant to whatever reason for which they are being discussed.

That sounds a bit circular and pithy, so here's an example: there was a man named Tiro in Ancient Rome, who was the slave and companion of a famous lawyer of the time. We have several sources telling us various things about Tiro - what he did, when he did it. None of them indicate anything at all about his gender or sexual preferences. Asking whether he was cis or otherwise is an unanswerable question, because we just don't know. He's consistently referred to as a "he" in all the evidence we've got, and that's as far as we can get. Perhaps he was trans and the fact was simply never recorded. Postulating one way or another is just conjecture, and outside the historian's realm.

Sources:

For Roman ideas on homosexuality: Roman Homosexuality: Ideologies of Masculinity in Classical Antiquity - Craig Williams

For examples on accusations of homosexuality in the past, see anything from Cicero's Philippics (especially 2) to The Trial of the Templars by Malcolm Barber to the case of Fred Richman, US congressman in the 1970s, in this article.

This answer by /u/Algernon_Asimov goes into the historical evidence of homosexual/homoromantic behavior for two historical figures.

Otherwise, you might glean much from the FAQ on sexuality and gender identity.