The problem is the spaces you have around $position in the grep, as illustrated by the following test code:

my @priority = qw/RB1 RB2 FL1 FL2 QB1 QB2 TE1 WR1 WR2 DST/;
my $position = q{QB2}; 
# Print original list
print join q{ }, @priority;
# Process using original regex, with spaces 
@priority = grep {!/ $position / } @priority; 
print join q{ }, @priority; 
# Process using regex with spaces removed
@priority = grep {!/$position/ } @priority; 
print join q{ }, @priority;
[download]

RB1 RB2 FL1 FL2 QB1 QB2 TE1 WR1 WR2 DST
RB1 RB2 FL1 FL2 QB1 QB2 TE1 WR1 WR2 DST
RB1 RB2 FL1 FL2 QB1 TE1 WR1 WR2 DST
[download]

An alternative might be the /x regex modifier, which tells the regex parser to ignore most non-backslashed, non-character class whitespace.

Hope that helps.