If the visits are for the purpose of offering advice and cooperating in righteousness and piety, then this is something that is good and is enjoined in Islam. The Prophet (peace and blessings of Allaah be upon him) said: “Allaah says, ‘My Love becomes an entitlement for two who love one another for My sake, and two who visit one another for My sake, and two who sit with one another for My sake, and two who are generous to one another for My sake.’” Narrated by Imam Maalik (may Allaah have mercy on him) with a saheeh isnaad. And the Prophet (peace and blessings of Allaah be upon him) said: “There are seven whom Allaah will shade with His shade on the Day when there will be no shade but His,” among whom he mentioned, “two men who love one another for the sake of Allaah, meeting and parting on that basis.” The example given is that of two men, but the ruling is general and may apply to two men or two women. If the visit to a Muslim or Christian woman is for the purpose of da’wah, calling them to Allaah, and teaching them and guiding them to good things, and not for the purpose of worldly ambitions or taking the commands of Allaah lightly, then this is all good. If a Muslim woman visits her sister in Allaah and advises her to avoid tabarruj (wanton display) and unveiling, and to avoid being careless with regard to all the sins that Allaah has forbidden, or she visits a neighbour who is Christian or otherwise, such as a Buddhist etc., to advise her and teach her, this is something good and comes under the heading of the Prophet’s words, “Religion is sincerity (naseehah), religion is sincerity, religion is sincerity.”  If she accepts the advice, then praise be to Allaah; if she does not then you should give up the visits which do not serve any useful purpose.  

With regard to visits for worldly purposes such as leisure, idle talk or eating etc., it is not permissible to make such visits to kaafir women, whether they are Christian or otherwise, because this may lead to corruption of one’s religious commitment or morals, as the kaafirs are enemies to us, so we should not take them as close friends. But if the visit is for the purpose of daw’ah, calling them to Allaah, encouraging good and warning against evil, then this is something that is necessary, as stated above. And Allaah says in Soorat al-Mumtahanah (interpretation of the meaning): 

“Indeed there has been an excellent example for you in Ibraaheem (Abraham) and those with him, when they said to their people: ‘Verily, we are free from you and whatever you worship besides Allaah, we have rejected you, and there has started between us and you, hostility and hatred for ever until you believe in Allaah Alone’”

[al-Mumtahanah 60:4]