Edit: From Hetzer's comment below, I misused the phrase blood feud. What I meant by it was, "If the average citizen knew their ruler was a blood relative of the enemy's ruler, how did they feel that the war was partly an intra-family ( thanks, u/greengreen_grass! ) struggle."
I don't think the historical record supports the idea that the conflict was in any way a blood feud, or at least not in essence. The royal ties between (some) of the combatants did complicate things, but as shown in the excellent book The Sleepwalkers by Christopher Clark there were many powerful political forces at work that lead to the war, and most of them operated independent (to one degree or another) of royal authority.
What do you mean by 'blood feud'? If the implication is that the war was caused by something like 'sibling rivalry', then that is incorrect. The origins of WWI are difficult to pin down, but we can usually come to a consensus around the factors of: nationalism, alliances, and ethnic tensions.
Not to be persnickety, but it's an intra-family struggle.
Edit: I refer here only the to UK part of the question.
The familial ties would have been common knowledge. They really wouldn't have caused problems for people. The Monarchies weren't powerful by this point (in the UK, the King still sometimes used his veto on legislation and still influenced the Tories). They didn't really have a hand in things, and so there was no question as to what their motives were. They were simply figureheads to support or dislike.
The English people knew that the British royal family was related to the German (and also Russian). Remember, they were the house of Saxe-Coburg and Gotha until they changed it to the house of Windsor in order to distance themselves and divest themselves of those ties.
There is a reference to this in fiction, at least. In Trumbo's "Johnny Got His Gun", there's a passage about a Scottish soldier who threw down his gun because he realized there were Bavarians across the trench, led by Price Rupert, who was technically a Stuart, and, in his mind, his legitimate king.
I thought long ago that I came across a similar story that was actually historic, but was unable to find it upon searching.
Yes, the ancestries of the rulers were well known.
However, don't think it was a new or unusual situation. European monarchs had been marrying the daughters of other European monarchs for centuries. For example, Henry VIII's first wife Catherine of Aragon was the daughter of the King of Spain (and previously wife of Henry's late brother Arthur).