hello I've ran into the same problem a few times now when an idol try to talk to me (I believe about them deciding to graduate) the image of the idol will load and the background will get blurry but the idol's text never loads and I am still able to interact with the build and the menus on the side. It was never a big problem because of this because i could just click around a little till i got save and quit then i would reload and it would be back to normal, however i did miss out on whatever the idol was going to say. unfortunately the last time it happened i was no longer able to interact with the side menu thus i lost a good bit of progress.
If you need/want anymore info let me know. I look forward to build an idol empire in the future!