A better description for non-Australians about climbing Uluru might be:
In recent years there has been political recognition in Australia that the European settlers who came to the country in the 1700-1800’s did much harm to the original inhabitants of the land - the Aboriginal people. While the Aboriginal people are still very marginalised and many are disadvantaged, autonomy over the traditional lands that hold deep meaning for them is being recognised. Because of this, the climbing of Uluru will no longer be permitted as “the rock” is very sacred to them.
Tourists are still welcome to travel to see Uluru, just not to climb it.
Personally, I think that if you have a chance to go see it, the time of year is moot. Yes it might be hotter in January, but you’ll be in air conditioned vehicles and able to keep hydrated. And in places like Sydney (where I live) it’ll be gorgeous summer weather for enjoying the harbour and beaches at their best. ❤️