Is it permissible to marry a non-religious Jewish women?
How it is possible or how is it not-possible?
Judaism requires Jews to marry other Jews. But, like many laws, not everyone keeps this.
A religiously-observant Jewish man is allowed to marry a non-religiously-observant Jewish woman, but they will have to have some serious conversations -- for instance, if she doesn't keep kosher but he does, will the kitchen be kosher?
A non-observant Jewish man could certainly marry a non-observant Jewish woman. This one's relatively straightforward.
As for a non-Jewish man: Judaism prohibits intermarriage. Now sadly, there are plenty of non-observant Jewish women who marry non-Jewish men anyhow. Usually there will be conversations about how they will affiliate, and especially with which faith to raise the kids. (Jewish law views the children of a Jewish mother as always Jewish.) In some situations the husband may convert -- if he's sincere about it, great. Sometimes he may feel pressured to do a quickie conversion that he doesn't really believe in, which isn't ideal from the standpoint of Jewish law nor their relationship.
People are complicated!
Lastly, if the man is a Kohen (i.e. his ancestors were priests in the Temple), he's only allowed to marry a born-Jewish woman who was never divorced (widowed is okay), nor ever had a non-Jewish "boyfriend."