Magic has happened
We will notice this very quickly because those that are in charge with terminating accounts of all sorts will notice a sharp drop in work. Within less than 48 hours you can expect the news to break world wide.
This will cause immense upset (in the sense "commotion" and "attention"), because a verifiable magic event has happened for the first time in recorded history. And not just that a magician has for the first time pulled a rabbit out of an actually empty hat, but the entire planet has been subjected to this.
It is safe to say that pretty much everyone's attention will be aimed at this, trying to find answers to the obvious questions: Why has this happened? What, or who, has caused this? How long will the effects last?
Next comes the excitement and dread. Excitement that you may live on this Earth forever. Dread, for the exact same reason. Wait... what?! I am stuck on this...
Pale Blue Dot... a view of the Earth from the orbit of Pluto.
...like, forever? No Heaven? No rest? No shedding of this mortal flesh and ascending to the bliss of the afterlife?!
This is where the religions will be the most affected. Because not only does a lot of piety stem from our fear of dying, but also from our wariness of living on this amazing but also very small and sometimes quite dreary, dangerous and inhospitable ball of mud.
This subject alone can fill entire tomes of fiction because pretty much all religions are based on the assumption that a human life begins and then ends. The possible outcomes here are extremely broad and there is no way to tell what happens other than that there will be upheavals, where all religious institutions are standing gaping and desperately trying to make sense of the situation since people will be swarming them for answers... answers they do not have.
As for politics the same thing applies: this is a much too broad question to tell for sure. But the worry about over-crowding will most likely not be the first thing on people's minds. Instead you can expect there will be much resources spent on the questions I mentioned before: why, who, what, and for how long?
Next there will be much effort on trying to find out the actual consequences; the nitty-gritty details such as: have we only stopped dying, or have we also stopped aging? This will affect the upcoming actions a lot and before I go on to answer this question any further you need to set some parameters here or the answer will be too broad because there are too many possible outcomes.
So to summarize: this will be noticed quickly. There will be lots of attention directed at this magic event. People will be searching for answers about why this has happened, how long it will go on, and trying to find out the details of this. Religions will be left just as confused as the rest of us, and even more so when people demand answers from religion as well... answers they do not have. Politics is very hard to predict, apart from that we can expect government efforts to try to go to the bottom of this and help looking for answers.