Step 1: Group the four minerals by mineral class.
Monazite belongs to the phosphate mineral class. Natrolite belongs to the zeolite class. Spodumene belongs to the pyroxene class. Gibbsite belongs to the hydroxide class. Knowing the class tells us what elements each mineral typically hosts.
Step 2: Ask which mineral class is famous as an REE ore.
Among common industrial ore minerals, the light rare earth elements cerium, lanthanum and neodymium concentrate in certain phosphate and carbonate minerals. Monazite sand deposits are mined worldwide specifically for their rare earth content, along with thorium.
Step 3: Rule out the zeolite.
Natrolite is a framework aluminosilicate built from sodium, aluminium, silicon and water. Zeolites are known for ion exchange and molecular sieve behavior, not for hosting rare earths.
Step 4: Rule out the pyroxene.
Spodumene is mined as a lithium ore in pegmatites. Its chain silicate structure fits lithium and aluminium ions, and it does not act as a host for rare earth elements.
Step 5: Rule out the hydroxide.
Gibbsite is one of the aluminium hydroxide minerals that make up bauxite. It forms by intense chemical weathering and carries aluminium, not rare earths.
Step 6: Conclude.
Only the phosphate mineral, monazite, is a genuine REE bearing mineral among the four choices.
$\boxed{\text{Monazite}}$