The crime was similar to what happened at Sodom with Lot and the angels. The (male) mob’s primary target was to rape the Levite man. (A man, and a man set apart for God from birth, who had no land because God was his inheritance.) So it was seen as so bad that a Levite houseguest in the city should be demanded by a same-sex mob for sexual purposes, that it was actually better for them to mistreat his non-Levite wife because at least then it wasn’t “abomination.” But the mob then killing the woman with sexual mistreatment and not even trying to help her before leaving her for dead on the doorstep – that made it even more heinous than what the Sodom people managed. The Levite describes her fate as both a heinous crime and an “abomination.”
However, the men of Israel did go to Shiloh and consult God through lots: "And they arose and came to the house of God, that is, to Shiloh: and they consulted God, and said, “Who shall be first in our army to go to the battle against the children of Benjamin?” And the Lord answered them, “Let Judah be your leader.” (Judges 20:18)
However, the tribe of Benjamin at that time was prosperous and full of the notoriously awesome ambidextrous slingers and warriors, and apparently they were pretty sure they could beat the forces of the rest of Israel. Judges 13:21 suggests they weren’t wrong about that. The tribe of Benjamin also assembled and voted, and decided to stand by the criminals. They could have set an investigation in motion to find the specific men who were guilty, but apparently this was not done. This tends to say that the tribe of Benjamin at that time was not overly concerned about guest rights, mobs, married women, Levites, the opinion of the rest of Israel, God…
So after being beaten on the first day, the men of Israel consult God again: "Yet so that they first went up and wept before the Lord until night: and consulted him, and said, “Shall I go out any more to fight against the children of Benjamin my brethren, or not?” And He answered them, “Go up against them, and join battle.” (Judges 13:23)
Then Benjamin’s forces beat the tar out of the rest of Israel on the second day.
"Therefore all the children of Israel came to the house of God, and sat and wept before the Lord; and they fasted that day till the evening, and offered to him holocausts, and victims of peace offerings, and inquired of him concerning their state. At that time the Ark of the Covenant of the Lord was there, and Phinees the son of Eleazar the son of Aaron was over the house. So they consulted the Lord and said, “Shall we go out any more to fight against the children of Benjamin our brethren, or shall we cease?” And the Lord said to them, “Go up, for tomorrow I will deliver them into your hands.” (Judges 13:26-28)
So at this point we have established that the tribe of Benjamin have made themselves enemies of the Lord, and that they are cocky about their fighting prowess and not shy about engaging in civil war. The men of Israel are the underdogs fighting for law and order, and God is going to let them beat the tar out of Benjamin. (However, on some occasions when God put someone “into your hands,” that person was spared. God is again giving the men of Israel space for prudential judgment.)
The previous two days, Israel had lost 22,000 men and 18,000 men. On the third day, Benjamin lost 26,100 men and 18,000 men and 7000 men (the last two equalling 25,000 men). These are probably symbolic numbers, but it seems to indicate that the men of Israel caught up to the amount of their own casualties, but then added some on.
However, putting man and beast to the sword after the battle and then going around Benjamin’s land burning the cities and villages suggests that they were still scared of the effects of “abomination,” to the point that nothing could be looted or kept and none of Benjamin’s land could be redistributed. This was execution. However, nothing is explicitly said about any of this being God’s will.
Right after that, we have the men of Israel approaching God for help with preserving Benjamin as a tribe after all this punishment. And they weep and lament.
Then they also end up destroying the city of Jabesh Gilead, because they didn’t join in the fight against Benjamin and therefore must also have been okay with abomination; and only the virgin girls are allowed to live, so that the surviving members of Benjamin can wed with them. And then they have the weird thing with the daughters of Shiloh getting stolen for wives during the dancing for the Lord’s festival, apparently by prearrangement and possibly by previous consent of the daughters. (And maybe because they were mad at the priests, who knows?) But it seems like the rest of Israel decided to punish themselves as well as Benjamin, which means they must not have been comfy with what they did.
So “in those days everyone did what seemed right to himself” is pretty much the only way to sum it all up. Democracy in the ancient world could easily become associated with mobs and atrocities. Trying to follow the Law with zeal but without common sense could go too far. In this story, the Lord was consulted about some stuff but not about other things.** If the Lord’s favor is not explicitly quoted for stuff that the people decide for themselves, you can’t assume that He was in favor of it**.
(Granted, that’s not really an answer to the question in the OP.)