Suppose there are two groups, the As and the Bs. Some of the As are really bad actors. And some of the Bs are as well. But most of the members of both groups are tolerably well-behaved. Suppose there is a third group, the Cs. Some of the Cs comment on the bad behavior of the bad actors among the As and the Bs. But they comment in two very different ways. These commenting Cs attribute the bad behavior of the bad actors among the As to their being As,while they attribute the bad behavior of the bad actors among the Bs, not to their being Bs, but to factors that have nothing to do with their being Bs. The commentators among the Cs can be said to apply a double standard in respect of the As and the Bs as regards the etiology of their bad behavior. They employ one standard of explanation for the As, a different one for the Bs.
That's the schema, presented schematically. Instances of the schema are not hard to locate.
Consider cops, Muslims, and lefties. (Some leftists will complain about 'leftie' which I admit is slightly derisive. But these same people do not hesitate to refer to conservatives as teabaggers, right-wing nutjobs, etc., terms which are not just slightly derisive. Here then is another double standard. "We can apply any epithet we like to you, but you must always show us respect!" But I digress.)
So you've got your cops, your Muslims, and your lefties. The behavior of bad cops -- and there are such without a doubt -- is said by many lefties to derive from something 'institutional' or 'systemic' such as 'systemic racism.' Cops are racists qua cops, if not by nature, then by their professional acculturation in 'racist Amerika.' But the bad behavior of some Muslims, such as committing mass murder by driving jumbo jets into trade towers, or slaughtering those, such as the Charlie Hebdo porno-punks, who 'diss' their prophet, does not derive from anything having to do with Muslims qua Muslims such as their adherence to Muslim beliefs. A spectacular example is the case of Nidal Malik Hasan, the 2009 Fort Hood shooter who killed 13 people and wounded many more. His deed was dismissed by the Obama Administration as 'work place violence' when it was quite clearly a terrorist act motivated by Islamist beliefs. Wikipedia:
Once, while presenting what was supposed to be a medical lecture to other psychiatrists, Hasan talked about Islam, and said that, according to the Koran, non-believers would be sent to hell, decapitated, set on fire, and have burning oil poured down their throats. A Muslim psychiatrist in the audience raised his hand, and challenged Hasan's claims. According to the Associated Press, Hasan's lecture also "justified suicide bombings." In the summer of 2009, after completion of his programs, he was transferred to Fort Hood.
So here we have a double standard, an unjustified double standard. (Are double standards by definition unjustified? This is something to explore.)
Of course, there is a lot more to be said on this delightful topic. For example, police brutality does not derive from the professional training that cops receive. They are not trained to hunt down and kill "unarmed black teenagers" who are harmlessly walking down the street or "children" on the way to the candy store. But Muslim terrorism does derive from Muslim teachings. Not all Muslims are terrorists, of courses, but the terrorism of those Muslims who are terrorists is not accidental to their being Muslims.
Note the difference between
A Muslim who is a terrorist is not a true Muslim
A cop who is corrupt is not a true cop.
The first sentence is a clear example of the the No True Scotsman Fallacy. The second is not. Why not? Well, there is nothing in the cop-role that requires that a person who plays that role be corrupt. Quite to the contrary. But there is something in the Muslim-role, or at least the Muslim-role as presented by many teachers of Islam, that requires that players of this role make jihad against the infidel.