Is having sex on my period safe?

Yes, but..: It may be less comfortable because of the blood, which will interfere with lubrication, but many women will not experience this. Some women feel less comfortable, and their partner should respect this. But for the most, there is no danger at all.

Safe for what ?: Transfer of STD's remains the same. Pregnancy has been documented on any day of a woman's cycle including during menses. Those with irregular cycles are more at risk of this than those with stable patterns, but any exposure contains some risk.