The linesman in a soccer game, i.e., the person on the sidelines who
holds a flag and calls a ball out of bounds - is it proper protocol
for this person to ask all the players and parents to stand back from
the side of the field at least a few feet, so he / she can run back
and forth to properly carry out the position?

I'm not sure if its proper protocol but it sure seems like a
reasonable request to make.

The league probably even has a rule that people need to stand away
from the edge of the field.  It only makes sense.

?Linesman? is now an out-dated term. In modern times the ?Linesman?
has come to be known as the ?Assistant Referee?. According to the
official soccer LAWS OF THE GAME the referee has the authority to stop
the game if he or she encounters spectator interference.

THE OFFICIAL SOCCER SITE
http://www.drblank.com/slaw5.htm

Assuming the official viewed such encroachment as a sideline
disruption then yes, he or she has the authority to take corrective
actions, up to and including stopping the match until the problem is
resolved.

THE OFFICIAL SOCCER SITE
http://www.drblank.com/slaws.htm

How?s that?

Tutuzdad-ga

Those answers are pretty good.  I was concerned whether it was common
practice, or  at least acceptable practice, to politely but forcefully
ask the parents (and the players if necessary) to all step back at
least two or three feet from the sidelines so that I have room to move
back and forth along the sidelines.

I don't have much experience in soccer so I wasn't sure.

It is common practice only if the people standing on the side lines
are interferring with the assistant referee's ability to judge the
game.

It is courtesy for the audience to allow the assistant referee to
perform his duties by standing a few feet away from the line.  It is
up to the assistant referee to judge if the distance between the
audience and the side line is enough for him/her without interferring
his judgement/ability to make the correct call.

Dr. Blank appears to be in no way an official site for anything.  He
needs to  be smacked upside the head for calling his site official. 
Surely FIFA (www.fifa.com) is the most official ruling body for
soccer.  Of course individual leagues, surely the "little leagues",
can set their own rules.

Anyway, FIFA's laws are at http://www.fifa.com/en/laws/menu.htm

Thanks.  I guess I won't feel uncomfortable asking players and fans
(i.e., parents) to please step back a few feet.  Usually they are
right on the sideline.

Tutuzdad's information is correct (as is that on Dr. Blank's site,
regardless of it's not being "official").
In games under FIFA rules, coaches and reserve players have to remain
in the "tactical area" in front of the bench  - with a few exceptions.
 Coaches have been sent to the stands for ignoring warnings to observe
this.
As an assistant referee, you should know the all the rules, but at
your level, I can understand that referee training may be minimal.
If this is a recurring problem, I think it would be appropriate for
the league officials to get the word out to parents on proper fan
etiquette, and also have the referees speak to them before games  -
once or twice should be sufficient, with the warning that play will be
suspended or the game maybe terminated, especially if there is more
than inadvertant interference with the refereeing.
The kids will understand; they want to play by the rules that apply
for their heroes.

Thanks for all the information.  Yes, the training I received was
definitely minimal.  It basically consisted of me agreeing to be the
linesman / assistant referee (since there were no other parent
volunteers) and someone handing me a flag.