Is it OK to suck the breast of a breast cancer affected woman or HIV affected woman?

In general, yes it is safe. But there are exceptions based on the conditions.

A woman who is developing breast cancer might be excreting small amounts of fluids from the nipples. A woman who is lactating (to feed babies) is also ‘leaking’ fluids. Now, whenever a fluid is exchanged between two bodies there’s a risk of transferring something from one person to the other. If the woman is healthy then there’s no risk. If a woman has HIV then she can transfer the virus through breastfeeding, but these risks are quite low if the mother is on anti-retroviral drugs.

The chances of infecting an infant without treatment are 15% to 45% but with treatment, the risk goes below 1%. It still means that sucking the breasts of 100% HIV-infected lactating woman isn’t a smart thing to do.

But HIV isn’t the only transmittable disease. Others can be transmitted more easily, especially any bacterial or fungal infection. Again, the risks are small, but there are risks.