GR and QFT essentially have to meet at black holes and this is where you’d expect to find an anomaly with ought to help open doors to new physics, but what we see here is that this observation seems to still obey GR just fine and a a closer look will be necessary to find any anomaly.

It might just not be possible to see anything odd without having a black hole right there to study, but there’s always hope that the next new observation will provide a clue as the previous ones repeatedly have not.

Brian Greene's "The Elegant Universe" does a very good, completely non-technical, job of explaining the conflict between the two theories. It then goes on to explain why String Theory is one possible solution to the problem.

Here are a few that might help:

https://gizmodo.com/why-cant-einstein-and-quantum-mechanics-...

https://www.theguardian.com/news/2015/nov/04/relativity-quan...

https://en.wikipedia.org/wiki/Problem_of_time

https://physics.stackexchange.com/questions/387/a-list-of-in...

For a good general source if you want to learn a lot more from a good popular science point of view (but one that takes great care to not accidentally mislead by oversimplification as often happens with popular science) about general relativity and quantum mechanics, try PBS Space Time, especially after Dr. Matt O'Dowd took over as host and main writer.

https://www.youtube.com/c/pbsspacetime

I liked Sean Carroll's take on this with Steven Strogatz in the recent episode of Joy of Why.

https://www.quantamagazine.org/where-do-space-time-and-gravi...

tl;dr they don't conflict with each other, they conflict with a third assumption that particles have zero size. GR suggests they would be black holes, and those have mathematical difficulties. String theory is an attempt to model particles of finite size and thus eliminate black holes.

Black holes are extreme enough to be one of the places where both can matter.