The only cases of homeschooling I have found on the Internet for Sweden are when the child has been so mentally, physically or emotionally challenged that normal schooling has been judged as impossible. In all those cases, the community school board has to set up a plan of study, to see to that the national curriculum is followed, and supply the teachers.
Religion is no reason for homeschooling, because the curriculum is religiously neutral. Nowadays, several religions are studied in the subject Religion, which centers on mutual understanding. For the extremely rare case that the pupil's parents believe in creationism (and in those cases, they will probably be Jehova's Witnesses), the biology teacher will say "I respect your views, but this is the way I teach the subject and you'd better learn it that way to get a passing grade".
School is compulsory between the ages 7 and 16. It is the duty of the local school board to see to that everyone in this range gets schooling according to the national curriculum.
I have found no provisions or possibilities for home schooling in other cases than those mentioned. If allowed, the parents would then probably have to 1) present very good reasons, 2) prove that they have access to sufficient expertise in teaching and in all subjects to guarantee that the national curriculum will be adhered to.