Well it had be revealed at one point and even in the books it will probably occur somewhere towards the end, however in the books it will definitely be different. The producers took quite a few liberties here most likely for dramatic purposes.
If Jon marries Daenarys any political implications of his heritage are neutralized either way and might even work in Dany's favor. Randyll Tarly already said it: to many Dany is just a foreigner. Jon on the other hand was raised by Eddard Stark, a man who was widely respected and the head of one of the great houses. Jon was a member of the Night's Watch and a battle-hardened veteran at a very young age. On top of that he has a much stronger legal claim on the Iron Throne than Dany. All in all it can only reenforce Dany's position unless of course Jon wants to be crowned himself, which is unlikely.
To be honest I don't think this specifically will cause that much problems for the simple reason there's only one season left and that's kinda short to create that big of a rift between Jon and Dany. For all we know this might even be only revealed all the way at the end. Tyrion already brought up the issue of succession. It has been speculated that Dany might become pregnant of Jon, thus solving this problem, but another possibility is that she might not make it and makes Jon her heir.
Jon's real name also has a strong symbolic meaning. Aegon I was the one who forged a single empire from 6 of the 7 kingdoms and this is what has to be done again if they want to survive. What's more Jon had an identity crisis his entire life, so his real name is vital for him to understand who he truly is.
Jon made Daenerys and 3 dragons fly beyond the wall. So the night king has the chance to kill one and use it to burn down the wall.They got one dragon killed just for a zombie to show Cersei so they can ally with her and fight the dead.Cersei asked him not to take a side. But Jon said no blaaa blaah honor this honor that. its like saying help us take down the army of the dead so that we can kill you later, In context of Jon he was hoping to ally with Cersei so badly even taking risk of his own life and cost a dragon, and saying these words to her face but still expecting her to fight with him. this is why i think hes the worst character . .
It was Daenerys who pretty much forced Jon to go beyond the wall in the first place and it was Daenarys herself who decided to pick them up again. She even admitted she didn't believe his story until she saw it with her own eyes. It's also kinda unfair to blame them for not taking into account the possibility that the Night King might be able to fell a flying dragon with a single javelin. The fact that was able to do that, means he would have gotten past the wall either way. Having Viserion just made it easier, both for him as the producers.
And really it doesn't matter whether Jon would have lied or spoken the truth. Seriously you are implying that Cersei cared about that. Despite having seen a Whight and given her word that she would send her armies, she has no intention of doing so. Had Jon lied she wouldn't have believed him and laughed if he actually would honor his word. Jon pretty much hit the nail on the head when he said that when people endlessly lie to each other, words become completely meaningless.
Because Jon spoke the truth, his faction actually was the moral victor of the meeting. Cersei had already made up her mind beforehand, she made it clear her word means nothing and that she only cares about herself, with other words she is unworthy to rule. Jon on the other hand showed that he will fight for the realm and wants to be a just and fair person. Not merely to sprout hollow words like "honor", but because it's, as Theon said, the right thing to do. This also led to Jaime abandoning Cersei, now she has no one left. At this very moment she's just scheming and lying for the sake of scheming and lying.
Saying that Jon is the worst character for not doing the thing everyone has been doing the entire series and which led them to be in such a dire situation really doesn't make any sense. You can't form a unified alliance against the doom of mankind based on lies.