Compared to the environment Hashirama and Madara grew up in, Naruto lived a relatively easier life – he was admittedly ostracized and all that, but at least he didn’t get killed at the age of 7 in a place where the average life expectancy was 30 years old. There must have been a large number of clans back then, who regularly fought each other over things like territory – it was the Narutoverse’s own Sengoku period, with clans like the Uchiha or Senju emerging as some of the more powerful groups. They exist in Naruto’s time as mini-factions within villages too, so I guess various clans banded to form villages – like how the Nara or the Sarutobi have their own compounds within Konoha. Even so, conflict still did exist both between and within villages in the form of all sorts of wars and violence, even after places like Konoha or Suna were formed – so Hashirama only partially succeeded in achieving his definition of “peace”. And ironically, it was Madara’s desire for destruction that ended up banding the shinobi world together, forming an alliance beyond what either Hashirama or Madara could achieve during their lifetimes.
It was surprising to see Madara so friendly when he was younger – maybe it was before he became corrupted by hate or something. To be honest, their refusal to tell each other their last names should have rung alarm bells instantly – in that sort of time period, I think it would have been more strange to find a kid playing by the river who wasn’t a shinobi. Especially when the Uchiha are so easily identifiable. Or perhaps both of them knew, but wanted to remain friends regardless – after all, Hashirama couldn’t find anyone else in the ironically named Senju clan of love who shared his idealistic views. And making ties between bitter enemies like the Uchiha and Senju would be the first step to Hashirama’s dream of a proper alliance. Madara is a smart guy, so I’m sure he knew perfectly well – but just happened to be more amiable as a child, I suppose. Their relationship was very much like with Naruto and Sasuke (or Kakashi and Obito to a lesser extent), all the way up until a fateful match at the Valley of the End. Madara was also willing to open up to Hashirama somewhat – which will probably change with Izuna’s death in the near future.
Nothing good is going to come of Hashirama tailing Madara at their next meeting – and Tobirama was a bit of a dick to obey orders without question and spy on Hashirama. I won’t say his hatred of the Uchiha isn’t justified though.