This issue happened with us also. After an investigation it turned out that the alignment on the 'p' html tag is not working well. But if you update the 'p' to 'div' manually with the source code editor in mosaico, the alignment works well again. This workaround needs a lot of manual work, in addition it is easy to make mistakes.
The mosaico extension provides an option for changing the behavior of the editor. If you set the
$config['tinymceConfig']['forced_root_block'] = 'div'; setting, the editor will start creating the new paragraphs as div by default. It was nice, but we faced another issue. In the mosaico templates the paragraphs are defined with 'p' tags. If your cursor is in a 'p' paragraph, and you press enter it defines a new paragraph, but the tag is inherited from the previous paragraph, so that it is 'p'.
So the final solution was a new mosaico base template where we replaced the 'p' tags to 'div'.