Maybe you meant King Solomon had relations with gentile women... I found this:
http://www.beingjewish.com/identity/kingdavidjew.html
Some argue that "there was no conversion process back then." I must wonder how they know this. They simply mean to say that they do not believe that the Laws of Judaism existed back then, and therefore it was okay to marry Gentile women. This entails ignoring the Torah's Commandment not to marry Gentiles.
Not only that, but the great people of Jewish history certainly did not consider it permitted to marry unconverted Gentiles.
Let's take Moses, for example. Moses was married to an Ethiopian woman, Zipporah. Yet when the soldiers brought back Gentile women from Midian, Moses got angry at them (Numbers 31:14-15). What was the difference? The difference is that Zipporah converted to Judaism.
How do we know that Zipporah converted? Because we know that she kept the Commandments. When Moses failed to circumcise his son because he was afraid that the traveling would kill him, what did Zipporah do? "Zipporah took a (sharp) rock and cut off the foreskin of her son..." (Exodus 4:25). Evidently, Zipporah was an observant Jew.
Intermarriage is also mentioned in 1 Kings, Chapter 11:
King Solomon loved many Gentile women, such as the daughter of Pharaoh, Moabite, Amonite, Edomite, Sidonite, and Hittite women. They are Gentiles, about whom Hashem told the Children of Israel "Do not intermarry with them and do not let them intermarry with you, for they will surely influence you towards their religions." Those are the people that Solomon clung to in love. He had seven hundred queen-wives, and three hundred concubines, and these women influenced him.
When Solomon grew old, his wives influenced him towards their gods, and thus his heart was not complete in his service of Hashem, as his father David's was....
Hashem said to Solomon, Since this is the way you are, and you have not fully obeyed My covenant and My Laws that I commanded you, I shall tear part of the kingdom from you, and I will give it to one of your subjects. I shall not do this in your lifetime, for the sake of your father David. I shall tear it away from your son.
We see here that the prophets considered what King Solomon did, in marrying Gentile women, to be a sin. Had they fully and properly converted, they would not have influenced him away from Hashem. (Bear in mind that the Talmud says that King Solomon never actually worshipped any idols, but since he did not stop his wives from doing so when he could have, Hashem considered it as if it were King Solomon's own sin.)
Even back then, evidently, there was a process of conversion. I think, then, that we have amply proven that Ruth was a convert, just like Sarah, Rebecca, Leah, Rachel, Bilha, and Zilpah. And as I said above, in any case the nationality of Ruth would not have thrown into question the Jewishness of King David, who was her great-grandson.