Polyester and Acrylic
It depends on weather. You can wear polyester all year long but acrylic in summer will be very difficult to wear. Acrylic is considered as a replacement for natural wool and polyester though non absorbant could work in hot weather . if it based on microfibers which increases wicking and quick evaporation .
Most important thing to remember is that both are synthetic fibers, and can be altered according to our needs. You can have a polyester Jersey which will literally melt You in summer and another polyester Jersey will make you feel like flying in the clouds in same hot weather. As general rule, if tshirt very think and draps like silk fiber, then it is good for summer if it doesnt drap, means it is made out of coarse/thick fibers.
However, acrylic has certain plastic type feel due to its low absorbency, so if you wear thick acrylic shirt in summer, it will make you feel like drowning in your own sweat due to lack of wicking and evaporation but, micro fiber acrylic shirt could work.
In addition to yarn and weave count, Another way to modify properties of synthetic fibers is during manufacturing where certain shapes leads to certain properties. Like flat/tape fiber will have good lusture and less wicking, round fiber will have less lusture and high wicking, and so on..