The tools aren't trying to talk to a URL on the internet.
When you launch the tools, ArcMap is actually constructing tool pages in HTML (this is an incredibly simplified explanation). Anyways, the point is it makes use of ActiveX and HTML to show these tool dialogues, as such your Internet Settings on the machine come into play.
There are a lot of Esri ...
I'd make use of Validate Table Name and GISPro's Alter Domain. You can alter your domain names using Validate Table Name to remove spaces.
Untested since I don't have ArcGIS Pro:
inGdb = r"Domained\gdb"
outGdb = r"output\gdb"
print ("listing domains")
domains = [d.name for d in arcpy.da.ListDomains (inGdb)]...