Here's the question: If I have a relative whose breast cancer was likely caused from hormone replacement therapy for menopause, will taking birth control pills, or any kind of hormone replacement therapy affect me?
Oy, what a heavy question for the Science Lady! It is important, though. Firstly, you rightly stated that your relative's breast cancer "was likely caused by hormone replacement therapy." It is true that "likely" is the best we can do, since the causes of breast cancer are so complex. Hormone replacement therapy (HRT) in menopause does increase a woman's risk for breast cancer, however, their are some studies with alternative hormones and doses that show promise. Also, some small studies have shown that women who start HRT during perimenopause do not suffer the same increase in breast cancer risk as women who start HRT later, after their natural estrogen levels have dropped significantly. Right now, it is best to avoid HRT if you possibly can, but the actual increase in risk is not extreme. Women on combined HRT have about a 5-6% increase in breast cancer risk than women not taking HRT. The American Cancer Society has a nice page on HRT here: http://www.cancer.org/cancer/cancercauses/othercarcinogens/medicaltreatments/menopausal-hormone-replacement-therapy-and-cancer-risk
Since your relative may have had breast cancer due to HRT, you should be extra cautious. It also matters whether the relative was your mother, grandmother, aunt, or sibling, and if other family members have taken HRT successfully.
Now for birth control pills. Some studies have shown a slight increase in breast cancer risk with long term (greater than 10 years) use of birth control pills. However, the increase is very slight and has not been found in every study. It is likely that the increase in risk is very small for women who do not carry BRCA1/BRCA2 breast cancer mutations. Plus a lot of these studies were done in women taking birth control prior to 1975, when hormone doses were much higher than today's low-dose pills. Birth control pills have been shown to actually decrease uterine and ovarian cancer risk, so there's a plus. However, they do carry a risk of blood clots. A family history of blood clots, stroke, clotting disorders, and current or former smokers should avoid birth control pills. All in all, The Pill is the most studied and widely used drug of all time (except for perhaps aspirin), and it is unlikely there are any more surprises for us. The Patch has been found to have a higher risk of blood clots than the pill. Also, there are new low-dose intrauterine devices (IUDs) that are even lower risk than the pill or any other method in terms of side effects and cancer risk.