Kombucha needs some airflow to ferment properly, but it shouldn't be completely open to the air. Cover the jar with a breathable cloth secured with a rubber band.
Kombucha fermentation relies on a symbiotic culture of bacteria and yeast (SCOBY). The yeast needs oxygen to produce alcohol, which the bacteria then convert into acetic acid and other beneficial acids. A tightly sealed jar would prevent this process, leading to a stalled or unhealthy fermentation. However, leaving the jar completely open invites fruit flies and other contaminants. The ideal solution is to use a breathable cloth, such as cheesecloth, muslin, or a tightly woven tea towel, secured with a rubber band. This allows for airflow while preventing unwanted pests and debris from entering your kombucha. The cloth should have a tight enough weave to prevent fruit flies from getting through.
Sanitize your cloth cover by boiling it for a few minutes before each batch to minimize the risk of mold or other unwanted bacteria contaminating your kombucha.