Should sex be avoided while having breakthrough bleeding?

Sex and bleeding: Sorry to say, but depends on whether or not you have been thoroughly evaluated. Btb is generally a term for irregular spotting on hormonal contraception. Hopefully, your md has already evaluated you for cervical dysplasia, endometrial polyps, fibroids, vaginitis, hormonal imbalance, and other causes of abnormal spotting. If you truly have btb, then whether to have sex is up to you & your partner.

Personal preference: Intercourse will be "messy" but some find it "necessary".- i would skip the "dining out" portion(cunnilingus-oral sex) as the cervical os may be open and the mouth contains some highly disease producing(pathogenic) bacteria that could find their way into the uterus causing an infection.

Not necessary: This is more of a personal choice. Medically it is not unhealthy to have intercourse on your menses or with breakthrough bleeding. Many couples will only have intercourse on their menses because then they know they can't get pregnant. But if this is not acceptable to you or your partner just avoid those days.