To say "kyrka är öppen alltid" is ungrammatical because 1) it sounds really strange to say just "kyrka" and 2) it sounds strange too to put the adverb at the end.
"Kyrka" in singular indefinite is just not used for "church in general" the way English uses it.
This is actually what my mormor would have said ("kyrka är alltid öppen"), which means that "kyrka" used to be a feminine noun I suppose :). (She would never write like that of course.)