Is it illegal to quote online poetry?

Not illegal. Poetry works generally belong to the category of copyright, and the copyright law stipulates that when quoting other people's works, the author's name, the name of the work and other information should be indicated, and the legitimate rights and interests of the copyright owner should not be infringed. Therefore, if quoting online poetry, indicating the author's name and the title of the work, does not infringe the legitimate rights and interests of the copyright owner, it does not constitute infringement.