Even though the Lord told the children of Israel not to marry into the pagan nations that surrounded them they did so anyway. He called the offspring of such unapproved marriages bastards. It took several generations before the descendants of such marriages were allowed back into the Lord's congregation (which is another name for the nation of Israel).
The reference from Judges 11:1-3 was not God's doing. Gilead fathered Jephthah by a harlot, as well as sons by his wife. When they grew up they chased Jephthah out of town because he was "the son of a strange woman" (verse 2). If you read the rest of the story you'll find their fortunes changed, and they called Jephthah back home to be their leader.
Finally, you asked about the meaning of 1Samuel 20:30, where King Saul is angry against his son Jonathan and screams at him some very unkind words. He yelled at his son and said 'How rebellious and faithless your mother was!' (1Samuel 20:30).
God had no part in what Saul said in 1Samuel 20:24 - 34. This was Saul's frustrated and angry tirade against his son whom he felt was siding with David (which meant against him). In today's language, Saul's statement to Jonathan would have the same meaning as "You son of a bitch." He accused Jonathan of favoring David over the king.
Our Creator is, without a doubt, no respecter of persons. The apostle Peter, a Jew, was speaking to a group of gentiles when he said that God does not respect one person over another but rather accepts anyone who is willing to listen to Him and do his will (Acts 10:34-35).
Gentiles, of course, have no choice as to who their parents are and neither does an illegitimate (born without the benefit of their parents being married) child. The apostle Peter, however, reminds us that if ANYONE, regardless of how they came into the world, fears God and does what is right, that they will be accepted. The nature of a person's birth has nothing whatsoever to do with whether or not they are ultimately saved. Being born out of wedlock does not matter, what really makes a difference is whether a person has a close and intimate relationship with our Father in heaven.