My question is more of an editorial question than a citation question. A website is treated as a book in a citation thus the title is italicized. This is absolutely sensible.
However, I come across genealogical reports or other work written by others in which a website is mentioned by title in the text but not in italics. Citations in the same piece of writing often will have the same title in italics.
When I edit a these I will "correct" the title by placing it in italics. Yesterday I tried to find a reference that supported this. The only reference I could find was in the Chicago Manual of Style (CMOS) which does not support it. (Apparently they went from no italics in the 15th edition, to using italics in the 16th, and are now back to no italics in the 17th.)
It seems to me that italicizing a website title in text should follow the same logic as in a citation.
Thus my question, what is the recommended practice and where can I find a reference besides CMOS?
(The writing in question is not for a journal publication with its own set of guidelines.)