This is an intriguing segment of the Scriptures.
One. Only Holy Scripture can assist us, at this time.
It is possible to defend both positions from Scriptures. However, as of right now, it is not possible to defend any position from outside Scripture.
The rabbinical text quoted by Bob Jones was written many centuries after the fact, and the author of that rabbinical text makes several grave errors. One such error is placing Jephthah in the same generation as Phinehas. Phinehas was from the time of Moses and Joshua. Jephthah lived some 300 to 400 years later.
We have no extra-biblical evidence or commentary from the days of the Judges, so far, which leaves us reliant on the Scriptures for clues to figure out what happened.
Two. Times of Renewal not Corruption.
I've read in many places that Jephthah lived in a very corrupt time-period, and that in his ignorance, or perhaps in his semi-pagan understanding, it was feasible that he might've killed his daughter.
Unfortunately for that line of argumentation, the Scriptures do not support it. On the contrary, Israel had just repented and turned to the Lord in a powerful way. Just 3 verses before Jephthah is introduced, we read this:
And the sons of Israel said to the LORD, We have sinned. Do You to us whatever is good in Your eyes; only deliver us, we pray You, today. And they put away the strange gods from among them, and served the LORD. And His soul was moved by the misery of Israel.* (Judges 10:15,16)
Finally, Jephthah's immense knowledge of Moses' and Joshua's writings lead to no other conclusion than that he knew very well that sacrificing (to death) a human would not in any way please God, and that he could offer an alternative sacrifice as provisioned in the Law (Lev. 27). His correspondence to the Ammonites in Judges 11 show his mastery of the Scriptures.
I don't claim to know what really happened, but it seems to me that he did not kill his daughter. There may have been another practice -- which involved virginity -- of which we are not aware today.
That Jewish writers, many centuries later, wrote that Jephthah did indeed kill his daughter only shows those writers' thought-patterns, not Jephthah's. Some Jewish authorities from intertestamental times made claims that the Torah existed before God and is more powerful than God, etc. It was against such people and ideas that Jesus stood against.
I hope this helps, or at least guides us in the right direction.
I personally believe the answer must be found in the Mosaic Law or in customs of the day that are unfamiliar to us. Lev. 27:2-8 seem to speak of sanctifying or dedicating people (humans), through a "special vow." This seems to indicate tabernacle service. (Yet, Samuel was sanctified in this way, and he married.) Could this be what Jephthah did, combined with some other practice of his day?
In contrast, Lev. 27:29 seems to speak of things and humans that are "devoted." And they cannot be redeemed, but put to death. Many commentators firmly believe that this is referring to pagan prisoners of war, in which case Jephthah's daughter would not qualify.
Arguments for both sides look for clues in the Hebrew of Judges 11 to know if it was a vow of "sanctifying" or "devoting."
Regardless, it seems obvious to me that something else is going on. We are missing a piece of the puzzle that is not given us. I believe she was not killed, but she was sanctified in a way that she could never be married. And this was celebrated or commemorized by Jewish women for some generations.