Each post/comment has a allow_replies parameter:
As written in https://developers.steem.io/apidefinitions/#broadcast_ops_comment_options, the parameter cannot be set with a comment_options operation.
After some digging, I found that the parameter was disabled on the 28 june 2016: https://github.com/steemit/steem/commit/5fcabd81b0f31862608533d2157e470f6db4e921.
with the comment:
Remove disable replies from comment_options_operation. Require 0 abs_rshares to set a max accepted payout. Added an extensions field to the op.
I found no reason why this change was made. I think it should be reverted and allow_replies should be added as parameter to comment_options again.
I opened an issue regarding this topic: https://github.com/steemit/steem/issues/3059.
Reply to the issue: