If a Jewish woman lived on an island without any other Jews & she was unable to leave or convert any of the locals, is she permitted to marry & have children? Would there be any difference or preference if the locals were Muslim, atheist, or idolaters?
Here are some Halachic considerations:
A Jewish woman is NOT obligated to marry and have children (Rambam Hichiot Ishut)
A Jewish woman can not marry a non-Jew unless he's properly converted.
Because a woman is [thought to be] passive in intimate relations (called קרקע עולם - the seabed), she's not considered transgressing if being fornicated forcefully, like in the Megilat Esther story. Therefore, she can cohabit and have kids in this way - subjugated to a non-Jew. Bonus: the kids are still considered 100% Jews.
Clarification, based on the above a Jewish woman should not prefer death to intimate relations with a non-Jew, unlike a Jewish man (also disputable).