For some reason both Mediawiki editor and TemplateStyles complains about background-position-x: 2px;. The property works even in IE6 so should be safe for supported browsers:
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In css-sanitizer, we generally add support for CSS properties based on published standards that are marked as being ready for implementation. background-position-x and background-position-y do not appear to be part of such a standard (yet).
Can you use background-position instead? That is allowed as part of CSS Backgrounds and Borders Module Level 3.
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I understand that position on adding properties, but normally when something is not standardized its kind of experimental. When it's experimental and can change the name can still be different etc... But that is different here. The property worked everywhere from ages. It will not change. It is already implemented. So there are simply no risks of change.
Bottom line is that it's just more convenient in some cases. The property works in all browsers that Wiki[mp]edia strives to support.