Building mosques and helping in that is one of the greatest of acts of worship before Allah. Participating with others in building these mosques is the kind of cooperation in righteousness and piety that is prescribed in Islam.
See the answer to question no. 146564
If that is in a Western country or any other non-Muslim country, then it is even more important to cooperate in doing that, because the Muslims there are in great need of that and because it makes it easier for the people living there to do acts of worship and encourages people to adhere to the rituals of Islam. And that also often plays a role in bringing non-believers to the faith. So the Muslims there should cooperate in such matters, so that their religion will become manifest among non-Muslims. There is nothing wrong with asking for charity to build a mosque or other things that the Muslims need, whether they ask in the mosques or in the marketplaces or any other place where people gather.
It was narrated from Abu Sa‘eed al-Khudri (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) went out on (Eid) al-Adha or al-Fitr to the prayer place, and when he had finished praying he exhorted the people and instructed them to give charity, saying: O people, give charity. Then he went to the women and said: O women, give charity… Narrated by al-Bukhaari, 1462
But that request for charity should be done without embarrassing others or putting pressure on them. Rather the teaching of the Prophet (blessings and peace of Allah be upon him) in such matters is to call on the people and encourage them to give in general terms, explaining to them the virtue of participating in that and hastening to do it. Then they should be left to decide what to do. There is nothing wrong with one of the people in charge of that making a special request to someone who he has ties with but, as we said, that should be done without embarrassing him or putting pressure on him or causing any hardship.
Shaykh Ibn Baaz (may Allah have mercy on him) was asked: We have a charitable fund for the mosque and there is a man who is allocated to looking after this fund; he takes the collection box around the rows of worshippers before the prayer begins, especially on Fridays. What is the ruling on doing this, especially since some of the worshippers feel somewhat embarrassed?
He replied: It depends, because what is meant is that he is asking of the worshippers and that may embarrass or annoy them. If he refrains from going around among them and asking them to put some money in this box for the mosque, that would be better. Otherwise the matter is broad in scope. If the imam says: The mosque needs your help, there is nothing wrong with that, because this is a charitable project. But taking the box around among their rows may cause some annoyance or embarrassment. So what I think is that it is better not to do that and just to announce that this box is for the mosque and whoever wants to may put something in it. You should not take it around among them or annoy them by doing so. This is more on the safe side and is a sounder practice.
And Allah knows best.