CKEditor table td style not showing in frontend
Had a similar issue for a long text field (filtered html format).

HTML tags were getting removed when switching between formats (editor was removing them).

At /admin/config/content/ckeditor/edit/Advanced (advanced is a profile name used for the filtered html format in my case), under "advanced content filter", choosing disabled solved the issue (server side filtering works, this filtering is there for the wysiwyg ux essentially).