I also had this issue with both IE and Chrome with the Identify tool. The IE console did not display an error message, but chrome did. What I was able to determine was when I upgraded to WAB 2.0, I was missing a file (LayerFieldChooser.js) at the location shown below. I checked my WAB 1.3 and it also did not have this file, I had to go to WAB 1.2 to find it. I copied it into WAB 2.0 and all seems to be working fine.
/webappbuilder/stemapp/jimu.js/dijit/LayerFieldChooser.js 404 (Not Found).