It is not permissible to make accusations without proof against a Muslim woman who does not wear hijab, or to pray that she go to Hell

Firstly: 

Undoubtedly not wearing hijab is a major sin, but it does not make it permissible for anyone to state categorically that the one who does not wear hijab is one of the people of Hell. Likewise, it is not permissible to pray against her in such terms, let alone indulge in impugning her honour and speaking ill of her. Rather what is prescribed in Islam is to pray for her that she be guided and her affairs set straight. 

Al-Bukhaari (6443) and Muslim (94) narrated from Abu Dharr (may Allah be pleased with him) from the Prophet (blessings and peace of Allah be upon him) that Jibreel (peace be upon him) said to him: “ ‘Give your ummah the glad tidings that whoever dies not associating anything with Allah will enter Paradise.’ I said: ‘O Jibreel, even if he steals and commits zina?’ He said: ‘Yes.’ I said: ‘Even if he steals and commits zina?’ He said: ‘Yes.’ I said: ‘Even if he steals and commits zina?’ He said: ‘Yes, and even if he drinks alcohol.’” 

The scholars of the Standing Committee said: 

The belief of Ahl as-Sunnah wa’l-Jamaa‘ah is that any Muslim who dies persisting in a major sin such as zina, slander or stealing is subject to the will of Allah, may He be glorified: if Allah wills, He will forgive him, and if Allah wills, He will punish him for the major sin that he was persisting in when he died, but his ultimate destination will be Paradise, because Allah, may He be glorified and exalted, says (interpretation of the meaning): “Verily, Allah forgives not that partners should be set up with him in worship, but He forgives except that (anything else) to whom He pleases” [an-Nisa’ 4:48]. And there are mutawaatir hadiths which indicate that the sinners among those who affirmed the Oneness of Allah will be brought forth from the Fire.

End quote from Fataawa al-Lajnah ad-Daa’imah (1/728) 

Please see also the answer to question no. 7436 

Abu Dawood (4906) narrated from Samurah ibn Jundub that the Prophet (blessings and peace of Allah be upon him) said: “Do not invoke the curse of Allah upon one another, or the wrath of Allah, or Hell.”

Classed as hasan by al-Albaani. 

It says in ‘Awn al-Ma‘bood: 

“Do not invoke the curse of Allah upon one another” means: do not curse one another, so no one should say to a particular Muslim: May the curse of Allah be upon you, for example.

“or the wrath of Allah”, by saying: May the wrath of Allah be upon you

“or Hell” by saying: May Allah admit you to the Fire, for example. It specifically mentions the prohibition on invoking such things upon particular individuals, because it is permissible to invoke curses in general terms, such as saying, May the curse of Allah be upon the disbelievers, or to invoke curses upon specific groups of people, or a specific disbeliever who died in a state of disbelief, such as Pharaoh or Abu Jahl. End quote. 

Please see also the answer to question no. 83390 and 36674

Thirdly: 

It is not permissible for a Muslim to accuse any Muslim man or woman of zina without proof as specified in sharee‘ah, namely four witnesses of good character, or a confession, or pregnancy in a woman who does not have a husband. Whoever does that has committed a major sin and deserves the hadd punishment for slander, which is eighty lashes on his back, and his testimony is never to be accepted in the future, and he is not to be described as being of good character, rather he is to be labelled as a faasiq (evildoer). 

Please see the answer to question no. 121059 . 

With regard to them saying that the “chaste women, who never even think of anything touching their chastity” are the women who stay in their husbands’ houses and wear hijab as prescribed in Islam, it may be noted that the verse in which Allah, may He be exalted, says (interpretation of the meaning): “Verily, those who accuse chaste women, who never even think of anything touching their chastity and are good believers, are cursed in this life and in the Hereafter, and for them will be a great torment” [an-Noor 24:23] refers to every chaste Muslim woman who refrains from zina and is not known to commit it. At-Tabari (may Allah have mercy on him) said: 

The “chaste women, who never even think of anything touching their chastity” are those who refrain from shameful deeds

“and are good believers” in Allah and His Messenger. 

End quote from Tafseer at-Tabari (19/138) 

It is not permissible to slander any Muslim woman who is not proven to have committed shameful deeds, even if the woman who is accused does not wear hijab. 

It says in al-Mawsoo‘ah al-Fiqhiyyah (2/227): 

The chaste individual (man or woman) whose accuser is to be subjected to the hadd punishment is the one who fulfils the following conditions, according to the consensus of the fuqaha’,if the accusation against him or her is of zina: 

1.He or she should be free; there is no hadd punishment for the one who makes accusations against a slave, male or female.

2.He or she should be Muslim; there is no hadd punishment for one who makes an accusation against an apostate or one who was originally a disbeliever.

3.He or she should be of sound mind.

4.He or she should be an adult.

5.He or she should be chaste. What is meant by being chaste is that the individual who is accused never had unlawful sexual intercourse, or intercourse within the framework of a marriage contract that is invalid according to scholarly consensus. If he or she was ever involved in any such deed, the description of chastity no longer applies.

 So chastity, in a practical sense, is a condition according to three (of the four) imams. 

However, Imam Ahmad said:

An individual may be described as chaste if he appears to refrain from zina. So if a person has never been proven to have committed zina, on the basis of evidence or a confession, and has never received a hadd punishment for zina, he is to be regarded as chaste. 

As there is no proof that this woman committed the crime of zina, she is regarded as chaste according to the rules of sharee‘ah, and the one who accused her without proof deserves to be subjected to the hadd punishment. The mere fact that she does not wear hijab does not cancel out the description of her as chaste. 

So how about if, in addition to that, she is as you described, keen to pray regularly and do good deeds, and memorise Qur’an? Such a woman is even more unlikely, in sha Allah, to do such evil things, and is more deserving of being well thought of; it is hoped that her prayer and the other good things that she does will keep her away from such shameful deeds, and we hope that by His grace, Allah will open the door of guidance to her, because of those good deeds, and she will begin to wear hijab as prescribed in Islam. 

Moreover, the hurtful things that they say about her in her absence are haraam; in fact this is a major sin, and if it is untrue, then it is a grievous lie. What people must do is fear Allah with regard to the honour of the Muslims, especially women and girls, because the impact of speaking ill of these people is immense, and she may be mistreated all her life because of something that was said against her out of animosity and enmity, and the one who said that word, or transmitted it, or approved of it, will bear the burden of that sin. 

Allah, may He be exalted, says, warning against such talk (interpretation of the meaning):

“And those who annoy believing men and women undeservedly, bear on themselves the crime of slander and plain sin” [al-Ahzaab 33:58]. 

The Messenger of Allah (blessings and peace of Allah be upon him) said: “Do not envy one another, do not artificially inflate prices, do not hate one another, do not turn away from one another, do not undercut one another. Be, O slaves of Allah, brothers. The Muslim is the brother of his fellow-Muslim. He does not wrong him, let him down or despise him. Piety (taqwa) is here” – and he pointed to his chest three times. “It is sufficient evil for a man to despise his Muslim brother. The whole of a Muslim is sacred to another Muslim, his blood, his wealth and his honour.”

Narrated by Muslim (2564) 

Please see also the answer to question no. 66699  . 

And Allah knows best.