Is Arc set to sign into AGOL atomatically? I had some crash issues with 10.6.1 when it was trying to boot up and log into AGOL.
Since Map was crashing, I had to open ArcCatalog and sign out, then was able to open ArcMap again.
Though, after this, I was also able to sign in again without crashing (I just don't check the sign in automatically box anymore).
R_