This whole idea, is, um, well... It is funny though.
Let's go, pretend we are aliens:
Assume 200 billion stars in the Milky Way. Assume 30% are near the sun's
sequence - F, G, K stars
Leaves 60 billion star systems with possible life on them. Exclude multiple
star systems and maybe we get 10 billion possible star systems kinda like
ours.
A three armed T-shirt made of alien_nylon has mass: 100g
(aliens wear size xtra-xtra small)
So we want to place just one T-shirt (where T stands for triarm I guess) in
each star system so another alien can find it floating somewhere in all of
vastness of the quadrillions of cubic kilometers in the star system.
So, we need 100g x 10^10 of alien_nylon. Or 10^9 Kg of alien_nylon.
DuPont makes 5.5 million tons of "earth nylon" per year. So we need
something like hundred thousand years+ of production of alien_nylon by the
AlienPlastics, Inc. company.
All of this just to leave one T-shirt in reasonable star systems -- where
they would be statistically almost impossible to find.
"I love this plan - let's do it." - would be the response of our alien
friends. Until they found out about distribution costs...