Perhaps it's a false dichotomy. What if the sport doesn't involve manual labor, like chess, or video gaming, or gambling?
Loosely, blue collar workers get paid by the hour, and perform manual labor. White collar workers, named because they often wore white collar shirts, are more likely salaried workers.
Professional athletes don't seem to fit squarely in either category. For example, uniforms could be equally be blue or white, or any other color, not to mention patterns, logos, and an infinite number of other variations. Uniforms usually don't have collars at all, and sometimes, for example, swimming, don't even include shirts.
We can distinguish white collar workers, from blue collar workers, and from those in the service sector.
There is a "three sector" hypothesis which proposes looking at the economy as composed of the "primary sector" (raw materials), "secondary sector" (manufacturing), and "tertiary sector" (services). There also other suggested "quaternary sector" (information generation and sharing, knowledge based services) and "quinary sector" (health, culture and research).
Not everything seems to fit into a few neat little boxes.
Professional sports could be considered part of the entertainment industry, and then, by some definitions, would fall in the "quaternary sector".
Good luck in this debate.