The only caution on a menstrual cup is if you use an IUD (i.e., Mirena or ParaGuard). Technically you aren't supposed to use a cup with an IUD. My sister does and hasn't had any issues - but I tend to err on the side of caution when it comes to those types of things.

I have a Mirena and generally do not have my period more than once a year. And it's lighter. And I have to think about birth control every 5 years.

I also have not yet taken the plunge into riding "correctly." Thinking this year may be the year to give it a go.