the primary role of a woman is NOT to raise children and be a homemaker.
There are millions of Muslim women who are not married and no kids. Are you saying they have no role?
If a woman is married, then her role maybe to take care of kids and home. But that is ONLY if a woman is married.
Islam is universal. we can't make sweeping generalizations that don't apply to all Muslims.
Women have many roles to play. Islam governs ethics, conduct and morality. So long as a working woman or stay at home woman abides by Islamic rules, working should make no difference. It is NOT axiomatic that if she works she is not abide by Islamic rules.
The reality is, many Muslim men, fathers, brothers, husbands, parents, etc do not follow Islamic guidance when it comes to their women, leaving woman no choice but to work. Some women have o work because tat is their only source of meeting people and interacting with society at large. Many many women. Eed to work in order to buy food, clothes, bus tickets, gas, medicine, books, things for their home, etc. nothing in this word is free. Nothing. If a woman wants to get married, a wedding usually costs some money (and Im not talking about a big fancy expensive wedding...just a simple one, but all brides like to wear a beautiful dress, invite their friends, have a gathering for lunch or dinner). These things are not free. You need o work to acquire money .