She wants to do ‘Umrah but she is afraid of crowding with men

Mixing between men and women is haraam. We have explained
that in detail in the answer to question no.
1200. 

Secondly: 

The rulings of Islam recognizes the nature of women and how
the Shaytaan exploits women’s charms, so the saheeh texts of Islam enjoin
women to stay in their houses and not to make a wanton display of
themselves, and not to crowd with men. Indeed, the Islamic texts do not
enjoin upon women what they enjoin upon men, such as attending Jumu’ah
prayers and prayers in congregation. 

Women crowding with men is one of the greatest causes of
fitnah, hence Islam closes the door to that temptation and protects acts of
worship from everything that could cancel them out. In the case of Eid
prayer, the Prophet (peace and blessings of Allaah be upon him)
commanded the women to go out to the prayer, but said that they should be in
their own prayer place, far away from the men. With regard to Hajj and
‘Umrah, Islam also forbids mixing between men and women, so that women will
be protected from crowding with men. This is clear from the following: 

1 – The Lawgiver has not enjoined Hajj or ‘Umrah upon a woman
unless she has a mahram with her. 

It was narrated that Ibn ‘Abbaas (may Allaah be pleased with
him) said: The Prophet (peace and blessings of Allaah be upon him)
said: “No woman should travel except with a mahram, and no man should enter
upon her unless she has a mahram with her.” A man said: “O Messenger of
Allaah, I want to go out with the army of such and such and my wife wants to
go for Hajj.” He said: “Go for Hajj with her.” Narrated by al-Bukhaari,
1763; Muslim, 1341. 

2 – The Lawgiver has granted a concession to a man who has
womenfolk with him, allowing him to leave Muzdalifah at night. 

It was narrated from ‘Abd-Allaah, the freed slave of Asma’,
that she stopped at night in Muzdalifah and stood there and prayed for a
while, then she said: “O my son, has the moon set?” I said: “No.” She prayed
for a while, then she said: “O my son, has the moon set?” I said: “Yes.” She
said: “Then move on.” We went on and she stoned the jamarah, then she came
back and prayed Fajr in Muzdalifah in her tent. I said to her: “O you! I
think we have come to Mina very early in the night.” She said: “O my son,
the Messenger of Allaah (peace and blessings of Allaah be upon him)
gave permission to the women to do that.” Narrated by al-Bukhaari, 1595.  

Imam al-Bukhaari included this hadeeth in a chapter entitled
“One who sends the weak members of his family ahead at night, so that they
may stand in Muzdalifah and make du’aa’, and move on when the moon sets.” 

3 – It is mustahabb for women to keep far away from the
Ka’bah when doing tawaaf, lest they mix with men, even if that keeping away
means that they cannot touch the Black Stone. 

It was narrated that ‘Ata’ said: The wives of the Prophet
(peace and blessings of Allaah be upon him) circumambulated the Ka’bah
with the men. It was said to him: “How come they are mixed with the men?’ He
said: “They did not mix with the men. ‘Aa’ishah used to do tawaaf far away
from the men, not mixing with them.” A woman said: “O Mother of the
Believers, let us go and touch the Black Stone!” She said: “Go yourself,”
and she refused to go. 

Ibn Jamaa’ah (may Allaah have mercy on him) said:  

One of the worst evil actions that the ignorant common folk
do in tawaaf is when men crowd with their wives whose faces are uncovered,
and that may happen at night when they are carrying lit candles in their
hands … We ask Allaah to inspire the authorities to put an end to this
evil. 

Ibn Hajar al-Haytami said, after quoting these words: 

Think about it, and you will realize that it is obligatory to
prevent women even from tawaaf if they do things that lead to fitnah. 

Al-Fataawa al-Fiqhiyyah, 1/201,
202 

Thirdly: 

If a woman wants to go for ‘Umrah, she has to travel with a
mahram who can look after her and protect her. She should choose times when
the Haram is not crowded. As for times when there is crowding, such as
Ramadaan, it is better for her to avoid doing ‘Umrah at such times, because
of the crowding with men that takes place, when she will not be able to
avoid them. 

In the answer to question no.
36514 we have quoted the words
of Shaykh Ibn Baaz (may Allaah have mercy on him), where he says that it is
better for a woman nowadays, in view of the intense crowding, not to do Hajj
repeatedly, because that is better for her religious commitment. 

And Allaah knows best.