Arguments made by Jews? Can you cite some examples?
Karaism is not "Torah-true Jews." Karaism is a heretical sect founded in the eighth century CE, by a disgruntled wealthy Jew named Anan ben David. Because he lost in a bid to become Exilarch (political liason between the Jewish community and the Caliph's court [and prior to that, the Sassanid Emperor's court]), he founded his own sect, which he claimed without any foundation or basis was a revival of Sadducee Judaism, a literalist sect that had died out in the second century CE (six hundred years earlier). Karaites, in any case, are not strict literalists, but follow a set of interpretive guidelines that their own scholars have come up with. Nor is there any proof that the original Sadducees were strict literalists without any interpretive guidelines of their own.
In any case, none of this is relevant to Jonah, who was a Jew (Hebrew, Israelite, whatever name we want to pick), whether affiliation was deemed patrilineally or matrilineally in his day. He says clearly in his book that he is a Hebrew. Again, Jonah 1:9--
ויאמר אליהם עברי אנכי ואת־ה' אלהי השמים אני ירא אשר־עשה את־הים ואת־היבשה׃
"He said to them, I am a Hebrew, and I hold in awe YHVH the God of Heaven, who made both sea and land."