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 ...
Assuming you need the field objects (and not just the field names)...
You could use a list comprehension. For example:
for field in [f for f in field_list if f.name in select_cols]:
Or without a list comprehension, it could be done like:
for field in field_list:
if field.name not in select_cols: