Another reason that many accept medical conspiracies is that they're plausible and seem to have a grain of truth to them. Suspicions about motives of governments and big business are legitimate and healthy.
The government does not always work in the best interest of its citizens, and huge industries ("Big Oil," "Big Pharma," etc.) are indeed motivated by making a profit (as was conspiracy peddler and convicted felon Kevin Trudeau). The U.S. government has done unethical and illegal things ranging from biomedical research to unwarranted surveillance.
It is undeniable that some doctors and some medical corporations have in the past acted unethically. Examples include shameful events like the infamous Tuskegee Syphilis Study, in which hundreds of poor, illiterate black men were denied treatment for syphilis by government agencies in a medical study that spanned decades, and recently-revealed American syphilis experiments conducted in Guatemala in the late 1940s.
Thus, for many people it seems like a small leap from genuine wrongs committed by those acting on behalf of governments and powerful corporations to endorsing conspiracy theories. But it's actually a big leap, and that leap requires evidence, not just speculation and theories.
Some may laugh off these beliefs as silly or harmless, but in some cases conspiracy theories have done very real damage to innocent people: For example in the past few years dozens of polio vaccination workers in Pakistan were attacked and murdered because of conspiracy rumors that they were intentionally spreading disease or even trying to abduct children for their organs.