This is a polyester shirt.
Estimated persistence
≈ 20-200 years
Why it matters
Polyester is a petroleum-based synthetic fiber. So are nylon and acrylic. "Synthetic" here is not a style label, it is chemistry. You are wearing a flexible plastic filament. The main issue is not that it sits in a closet. It is that washing and drying loosen tiny fibers from the fabric.
Those fibers can pass through wastewater treatment and end up in rivers and oceans. Even when captured, they often move into sludge pathways and can still re-enter ecosystems. At the other end of the product life, synthetic textiles are difficult to recycle at scale, especially when blends are involved, so many are landfilled or burned.
Details
Mechanism
Polyester is an extruded plastic fiber. Friction, heat, and agitation during washing and drying loosen tiny strands from the fabric.
After disposal
Synthetic textiles are difficult to sort and recycle, especially when fiber blends are involved. Many are landfilled or burned, which means either long persistence or direct emissions.
Better substitutes
Natural fibers are often easier to manage at end of life, but the practical improvement is usually better buying and laundry habits. Buy fewer garments and keep them longer. For synthetics you already own, wash less often, use colder gentler cycles, and add a wash bag or microfiber filter if you want to reduce shedding.