Sync Up! is an exhibition about the connection between the lunar cycle and the hormonal cycle. During the exhibition, you have read and observed different 'evidence' supporting this claim: matching the lunar cycle with your own cycle has multiple benefits and there has even been scientific research about it.
Were you skeptical throughout the exhibition, and have you paid attention to details? For example, have you looked at the sources from the scientific paper, or read the affilation? Who are these researchers? Have you read the leaflet that comes with your pill?
You have every right to doubt this kind of research, but before you do, it is also important to look at what you compare it to. Current research about the hormonal cycle, menstruation and everything around that research topic is also something that misses a lot of information, research and development. In fact, this idea of a 'hormonal cycle' often deviates a lot from individuals, to a point that it cannot be taken as example anymore. This standard cycle that is in current books and prominent in research is imposed on people, but can often not provide support. Additionally, this gap in research leaves a lot of room for rumours, myths or blatant misinformation to spread.
A theory like the lunar cycle might not be so odd: if 'real' research cannot provide any grip on a person's cycle, then another inadequately researched theory could possibly fill the gap. The theory about the lunar cycle highlights the problem within the (clinical) research world by imposing inadequate research in the same manner.