Cancer, no.
HIV yes.
There are really two kinds of cancers. Juvenile, and the rest. Juvenile cancers affect children are typically rare by comparison. The other cancers have very little selective pressure against them since they happen later in life after people have already reproduced.
HIV is different. Some people are already extremely resistant to different types of HIV. If the virus went unchecked, they would have a major advantage.
But as long as retrovirals work, that won't happen.