Blocking continues after enabling snapshot isolation
If your intention is to avoid readers from blocking writers and visa-versa in the default READ_COMMITTED isolation level, turn on the READ_COMMITTED_SNAPSHOT database option.  This will cause row versioning instead of locking to be used to implement statement-level read consistency.

Although often confused, the ALLOW_SNAPSHOT_ISOLATION option is not related to READ_COMMITTED_SNAPSHOT.  ALLOW_SNAPSHOT_ISOLATION allows the separate SNAPSHOT isolation level to be used to provide multi-statement read consistency but code changes are required to use it.  The READ_COMMITTED_SNAPSHOT option provides statement-level read-consistency without code changes, although one should be aware of the implications the locking behavior have on apps that rely upon locking.