The phrase "Double standard" refers to "holding two
related (or perhaps "equivalent" would be a better word?) groups to different standards". For example, liking pizza but hating chocolate would not be a double standard, because the two things are totally different. But refusing to eat all pizza unless it comes from Dominoes might be - since Dominoes pizza is basically the same as any other American-style pizza.
Since, for example, shounen action anime and slice of life romance anime are totally different, watching one genre and not the other would not be a double standard.
Actually, now I think about it, just liking and disliking things doesn't necessarily count anyway. Eg. Say you were the boss of a company. You like one of your subordinates, but you don't like another. That's not a double standard; they're two different people with different personalities. A double standard would be if you required all your subordinates to achieve 80% efficiency to get a pay rise, except for one employee who only needs 50%.
Or more relevantly, if you only watched anime scored 8.0 or higher on MAL, except for anime made by SHAFT, which you watch if it's scored higher than 6.0. The groups (anime series) are all equivalent, and you're holding them all to the same objective quality standard, but you don't require anime by shaft to be as objectively good according to that standard as other anime. In other words, you'll watch it even if it's not as good.
Shohei-kun's examples are also good.
There you go, quick English lesson for you

It's a subtle distinction that's hard to understand (and harder to explain).