Menstrual periods are considered "dirty" in some cultures, but not essentially any dirtier than other human functions. If you introduce anything into the vagina during this time, it must be clean as the cervix is "open" to infection. On the positive side, orgasm during menstruation may alleviate menstrual cramps. Particularly cervical orgasm, or uterus orgasms which involves contractions of the uterus. The contractions subside leaving the uterus in a resting state. Uterus orgasms tend to result from masturbating the Anterior Cervical Fornix, or the dimple in front of the cervix. This requires long fingers, or a suitable replacement.
Otherwise the simple answer is yes, but keep it clean!
Dr.Goodlove(non-medical)
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Yup, if you're both happy to do that. It can be messy but sex is generally messy! but play safe though! If you don't know where she's been you don't really want to be playing with blood and ingesting it to be honest. She may well enjoy it more while she's menstruating too, by the way. Everything can feel much much nicer at this time in her cycle.
It is not recommended to finger a person while they are menstruating, as it can introduce bacteria and increase the risk of infections. It's best to wait until their period has ended to engage in any sexual activities.