The notion of the false dichotomy is often used when you point out the flaws of a group someone actually supports, and the reply sounds like "I know they are, but what am I?" This is most common when mentioning the flaws in Christians, such as their greed, arrogance, and terrorism.
By definition, telling someone to obey or suffer is terrorism, it is using fear to discourage dissent. Christians use this terrorist tactic to discourage doubt in their youth, which is child abuse and just as bad as what Islam does to their kids.
But when you point this put they always complain about Islam being bad, a red herring to distract from the Christian abuses. This is a false dichotomy, that by opposing one you are supporting the other, the Christians see Islam as competition for money and power so they garner complacency by convincing people that opposing christian abuses is the same as supporting Islamic abuses.
This is far from the truth, most atheist people oppose all abuses, whether Muslim, Judaic, or Christian. Many of us even oppose the delusion of a god as a whole, especially the use of terrorism to discourage kids from questioning the claims of their leaders.
It is the same thing as saying that if you don't like vanilla then you have to like chocolate. Or you could parallel it to saying that if you want guns regulated you support deregulating automobiles.
The parallel also appears in supporting political candidates. Regardless of where this false dichotomy is used, it is a dishonest attempt to avoid responsibility.