Nope, it is quite controlled...and safer than people think.
Most modern aircraft have recirculation system, which recycle up to 50% of cabin air. However, the recirculated air is passed through HEPA (high-efficiency particulate air) filters, of the type used in infectious disease hospitals and intensive care units, which trap dust particles, bacteria, fungi and viruses...including COVID-19.
The risk is from the persons near you, not the recirculated air. It is cleaner than the best hospital you could be in.