Is it permissible for the woman’s guardian to refuse to give her in marriage to someone who is compatible, because of some problems between the two families?

Praise be to Allah.

The Muslims should put an end to all disputes among themselves that may generate resentment and hatred. The believers are brothers and Allah has enjoined reconciliation between believers who are fighting. He also described them as brothers in the faith. 

So they should try to forget this resentment, especially if they have any measure of religious commitment, as it says in the question. If the guardian hopes that this marriage may be a means of removing that resentment and hatred, then he is enjoined to go ahead with arranging a marriage for two reasons: 

1.Because the woman has received a proposal from a man who is compatible

2.In order to try to deal with the hostility (between the families).

Al-Tirmidhi (1084) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “If one of you receives a marriage proposal (for his daughter or other female relative under his care) from one whose religious commitment and good character are pleasing to you, then give (your daughter or female relative) to him in marriage, for if you do not do that there will be turmoil in the land and a great deal of mischief.”

Classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

But if the guardian fears that there will be a renewal of the problems and that his daughter may be wronged and ill-treated by this family, and they will not treat her kindly, then in this case it is permissible for him to refuse this marriage, because the guardian is acting in the interests of the one who is under his guardianship, and her interests in this case are served by not marrying this man. 

And Allah knows best.