Were the Patriarchs Jewish?

Are Abraham, Isaac, and Jacob part of the righteous remnant of Israel even though they existed before the nation of Israel was formed?

If your question is: were the forefathers Jewish? The answer is that they are the prototype and the fathers of the people of Israel. There are two covenants, that of the forefathers (Breishit 15, 18; Tehilim 105, 9), and that when we left Egypt at Sinai (Shmot 24). The forefathers are like the top of the pyramid or family tree, where technically, they are still individuals (lacking the 2nd covenant), but they knew prophetically that the Chosen People of Israel will soon descend from them and receive the Torah for the 2nd covenant (Breishit 15, 13-16). Jacob and his 69 sons went down to Egypt, but his name had already been changed to “Israel” (Breishit 32, 28). ("Jewish" and "Israel" have been synonymous and interchangeable for 2,700 years, since the exile and loss of the 10 tribes which had seceded from Judah/Judea, and subsequently there's no need to differentiate between Judah and Israel) Accordingly, it really depends on what you mean in your question, because the answer is both: yes and not yet. [On the other hand, if you mean to ask: are the forefathers literally the “remnant of Israel”, you are basically asking a question about the English language, and the answer is no: a beginning is not a “remnant”. Because the forefathers died about 3,700 years ago, and the word “remnant” means: that which remains, say after the destruction of the Temple and exile, or after the Holocaust, and not the “beginning” of the people of Israel.]