Easton's Bible Dictionary further defines the Biblical use of "bastard" as:
"In the Old Testament the rendering of the Hebrew word mamzer', which means "polluted." In Deuteronomy 23:2, it occurs in the ordinary sense of illegitimate offspring. In Zechariah 9:6, the word is used in the sense of foreigner. From the history of Jephthah we learn that there were bastard offspring among the Jews (Judges 11:1-7). In Hebrews 12:8, the word (Greek nothoi) is used in its ordinary sense, and denotes those who do not share the privileges of God's children."
God had commanded the Israelites not to intermarry with the nations around them, but they did, and God called their offspring bastards. Many generations had to pass before his progeny could be allowed into the congregation of the Lord, 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. Let's briefly look at the passage:
"And the king sat upon his seat, as at other times, [even] upon a seat by the wall: and Jonathan arose, and Abner sat by Saul's side, and David's place was empty. . . . And it came to pass on the morrow, [which was] the second [day] of the month, that David's place was empty: and Saul said unto Jonathan his son, Wherefore cometh not the son of Jesse to meat, neither yesterday, nor to day? And Jonathan answered Saul, David earnestly asked [leave] of me [to go] to Bethlehem . . .
" . . . Then Saul's anger was kindled against Jonathan, and he said unto him, Thou son of the perverse rebellious [woman], do not I know that thou hast chosen the son of Jesse to thine own confusion, and unto the confusion of thy mother's nakedness? For as long as the son of Jesse liveth upon the ground, thou shalt not be established, nor thy kingdom. Wherefore now send and fetch him unto me, for he shall surely die." (1Samuel 20:25, 27-28, 30-31)
God had nothing to do with the reference from 1Samuel 20:24-34. This was an angry outburst by King Saul against his son Jonathan. In today's language Saul's statement to Jonathan that "Thou son of the perverse rebellious [woman]" would have the same meaning as "You son of a bitch." He accused Jonathan of favoring David over the king.
God is no respecter of persons. The apostle Peter, a Jew, was speaking to a group of gentiles when he said,
"Then Peter opened [his] mouth, and said, Of a truth I perceive that God is no respecter of persons: But in every nation he that feareth him, and worketh righteousness, is accepted with him. " (Acts 10:34-35)
The gentiles had no choice of their parentage, and neither does a child born out of wedlock. But Peter tells us that if a child fears God, and works righteousness, he or she is accepted by God.
The circumstances of one's birth has nothing to do with whether a person will be in God's kingdom. It is what he or she does with their life in relation to God that counts.