Even if you have enabled the YouTube video button in the forum WYSIWYG editor, the video is not shown in the forum post when a user fills all the necessary data for the Youtube video in the dialog and clicks OK.
The trick lies in the following setting which needs to be set on (either for the whole forum group or on a particular forum level):
Enable images in posts: Advanced dialog
You can find it in the CMS Desk -> Tools -> Forums -> Edit -> General tab.
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