I had the similar issue and did the following to work in our organisation. Probably not the way to go and needs to be modified or tested whenever the Portal for ArcGIS is upgraded or with any browser updates
On top of the SAML pop-up (screenshot 1), up on selecting the ADFS option, I do get one more additional IE pop-up in a new tab (screenshot 2) which can be closed after clicking on option “Yes” which in turn returns to parent window.
Currently, I made a change to the core Portal file to suppress the IE pop-up in the following path
Path: D:\Program Files\ArcGIS\Portal\webapps\arcgis#home\postsignin.html
Modification: Basically, code was already written in the file to suppress the pop-up, but the condition to enter into the code was incorrect. The existing condition in the code is, if (navigator.appName === "Microsoft Internet Explorer").
But, the navigator.appName reads as Netscape instead of IE acronym and failing to close the pop-up automatically. So, had to change the condition to verify the browser appName as “Netscape”, which did the work at the moment.
Environment: Windows 10, IE11, Portal for ArcGIS 10.6 (It’s the same code in 10.6.1 as well)
Update/Solution: According to the Compatibility changes, IE 11 returns the word “Netscape” for navigator.appName property, to reflect the HTML5 standards to match the behavior of other browsers.