New answers tagged http
It shouldn't. The unsecure warning comes about when a secured page incorporates non-secured elements. A canonical tag is a link, not an object to be incorporated into the page, so there's no reason why the padlock should care whether the URL it points to is http or https.
Web browsers do not care about canonical URLs. It is for search engine use only (specifically Google). Additionally, canonical URLs do not affect the loading or rendering of a web page. So no assets will be loaded over HTTP which is what would cause an insecure error message. So, no, they will not display any error message.
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