“Jewish” is just as much a “race” as “Polish” or “Finnish”. The adjectives’ application to ethnicities (or races, or cultures, or nations, or whatever you want to call them) usually predate their application to citizenships. Countries tend to be named for their dominant ethnic group, not the other way around. There were Finns before there was a Finland, Uzbeks before there was an Uzbekistan, etc.
“Not the whole hog.” --Jonathan Miller. 
Flemish.
I was wondering the same thing. I looked up the root of Jewish, and my question still wasn’t answered. So I put the question in Google, "Why Jew ish, Yid ish, Am ish. There are no countries by these names. Being English only means you’re from England. I don’t feel like the question was answered. I assumed it just happened over time, but I wondered why it became a name that meant one was " like a Jew ". I don’t mean to offend, but was curious.
Because -ish doesn’t always mean “like a”, it also means “is a”. Someone Swedish is a Swede, not like a swede. Words and parts of words can have multiple meanings.
I always clear my throat when I get that.
And I’m not a moderator. 
What a Walloon!
Other way 'round. England is so called because it’s where the Angles live. The “-ish” suffix indicates “of or belonging to, of the nature or character of”, and there are similar formations in all the Germanic languages. So an individual member of the nation of Angles was English, an individual member of of the nation of the Scots was Scottish, and so forth. Likewise the language associated with the nation of Angles was English.
So “Jewish” = of or belonging to, of the nature or character of, Jews.
The sense of “approaching the nature or character of, but not quite there” (a reddish colour, we’ll eat around elevenish) is a later development. It only occurs in English. In German the same sense is expressed with the suffix -lich.
Amish
What an Ultrawalloon!
panache45 season!
It also seems to be the case that in English, it is a little bit more genteel to say someone “is Jewish” rather than “is a Jew”, and similarly for other ethnicity that have an adjectival and noun form. Probably because so many ethnic slurs use the “is an <X>” form.
That structure is not limited to ethnic slurs, it’s used for insults in general.
Zombish, zombieish, or zombyish?
Funny, you don’t look Bluish.