Search engines and especially Google, don't like that. Search engines sees two different pages on the web, they spent time and resources, and imagine how many pages are on the web and how many may have issue like this.
It means a lot of extra resources and sometimes bad user experience. For that reason, Google penalize those pages that do not redirect one domain version, to their preferred. In SEO this is called duplicate content issue.
In Blogger, this can be set very easily. If you already have a domain name, and set the name servers, and everything is OK, when opening your domain with and without www, you can see that there are two same version of your website.
So go in Blogger, Settings and in the section Publishing, click edit on your address. You can see from the image bellow that the check box for redirection is clicked. You should do the same as that will redirect your non-www version to www.
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