A discussion about opening a bag of potato chips, according to various poskim, can be found on the YUTorah.org website. A related discussion by Rabbi Dovid Ostroff regarding tearing toilet paper is also available.
From the first link:
Furthermore, there may be no violation
of koreya here either: the Tosefta
(Shabbos 17:9), cited in the Mishnah
Berurah (314:25), allows tearing the
leather covering of a barrel without
concern for koreya, and many
understand the reason to be that even
if the covering is not destroyed, it
is batel (subordinate) to the barrel,
and tearing the covering is therefore
like the mere removing of a nut from
its shell (though see Chazon Ish above
and 61:2 for a different explanation).
Some poskim claim that our case is
comparable, and thus permit tearing
the bag (see Igros Moshe, Orach Chaim
1:122, R’ Neustadt in The Weekly
Halachah Discussion p.134-138, and
Tikunim u-Miluim to Shemiras Shabbos
ke-Hilchasah 9:11). Others (cited in
Shemiras Shabbos ke-Hilchasah, ad loc.
note 11) employ other factors for
leniency, combining the opinions that
the biblical prohibition of koreya
only applies when doing so al menas
litfor (in order to sew it later),
that it is not koreya when the tear
itself constitutes a tikkun, and that
koreya is not violated when tearing
one entity into two (rather than the
tear separating two attached items).
If we take this first reason, we can understand why it would not apply to toilet paper. It is not batel. I'm uncertain about how it differs given the other two reasons.