Just because some varmint bullets have plastic tips, doesn't mean that all bullets with plastic tips are varmint bullets.
Hornady, Nosler, Barnes, and Swift make excellent big game bullets with plastic tips.
I used plastic tipped 140 grain Nosler Ballistic Tip bullets in my 7mm Rem mag on my first South African hunt to kill a variety of Plains Game animals, including a Kudu, a Blue wildebeest, and a Gemsbok.
I used plastic tipped 160 grain Nosler Accubond bullets in my 7mm Rem mag on elk, muskox, caribou, and on another South African hunt to kill some more Plains Game animals.
I also used plastic tipped 168 grain Barnes TTSX bullets in my .300 Weatherby to kill elk, another variety of South African Plains Game animals, and a variety of New Zealand animals including a large Red deer stag.
I've been lucky enough to have drawn two Montana Shiras bull moose tags. I killed each of those bulls with a 180 grain Nosler Partition bullet.
Like Muley Hunter posted, for moose I would use at least a 180 grain bullet, especially at .300 RUM velocities.