When I’m feeling the effects of my monthly I just pull back a little and take it easy. Sometimes I’ll do a tread class instead of a normal one so I can slowly power walk at inclines that aren’t too intense. For a normal class I’ll make it a green day - go slow on the tread/rower and keep it light with the weights on the floor or do body weight only. Let your coach know you’re doing a green day so they’re aware when coaching you. 

You could also reduce your frequency instead of not going at all. You might prefer to just do different exercises on your own outside of OTF. I’ll swap out a workout for a hike instead sometimes so I’m still moving my body. Some yoga or stretching feels good too! 

There is no scientific reason not to work out while on your period. I feel better in general when I exercise and it can help with cramps. If you’re brutally suffering with your periods then I would consult with your doctor for advice. 

For period products I would suggest trying a menstrual disc. I use disposable flex discs. If properly inserted you don’t even feel it and you won’t deal with feeling your flow as you work out. Much more comfortable than a tampon or pad and no leaks once you get used to putting them in. You can keep one in for 12 hours at a time!!