I have ran into this issue on several occations. I have found blog hops and found new blogs to follow. I follow them. Then, when I go to comment on the blog, I keep getting asked to sign into my google account. When setting up your blog, if you don't want your readers or new followers to have this problem.... this is how you can ensure they don't.
1. Go to the settings for your blog.
2. Select the Comments section.
3. Be sure that the "Who can comment" is marked to everyone.
4. Be sure that the "Comment Form Placement" is marked with Embedded below post.
5. To ensure you don't have spam posted to your blog, turn on your comment moderation. This will give you the ability to check the comments before their actually shown on your blog.
I hope this brings a lot of those who have their settings set to Google User, the attention that some people may not have access to posting on your blog.
If you found this blog helpful, please leave a comment and pass on the word to others. Thank you.