The 403 error is generated by the WordFence security plugin, which is used to protect the blog against intrusion. It seems that WordFence is responding to posts containing multiple URLs with an action that it doesn’t have the necessary permissions to carry out, suggesting an underlying problem with the plugin configuration. Only the site admin can diagnose the precise cause and modify the settings accordingly.
The 403 error has been discussed previously in this forum. In that case, Kim Sanders-Fisher was having trouble posting lengthy commentaries with multiple URLs and the problem was solved by submitting the text in smaller chunks. That suggests that an effective workaround would be to avoid posting multiple links at once.