Yes, your reputation with the Bridge soldiers will eventually affect your reputation with all of the military faction, and if you keep trading with them you may find some unexpected friends around the Zone. It isn't hard to change Military's feelings toward you, however. Just shoot a few, and word will soon spread that perhaps you aren't quite as friendly as they had been told. This doesn't seem to affect the Bridge Soldiers, apparently they are more interested in maintaining their vodka racket than they are in fighting those who trade with them.
There are occasions when you have
to kill soldiers, even friendly ones, to succeed at a mission. I have had this happen
Then there are other cases where being neutral or even friendly can make missions much easier
It is up to you to decide when unexpected friendships become unwanted friendships.