You can control centering of DokuWiki text via a plugin, and can control centering of images through DokuWiki syntax. What you cannot do is to left/right/center tables.
This is because the "text-align" css property applies to inline content, not to a block-level element like "table". In order to center a table requires a modification to the table style to set "margin-left: auto; margin-right: auto;". Rather than building a new plugin, I would like to see the existing DokuWiki syntax upgraded in order to handle the table alignment syntax.. (Presently, you can align the fields in a table, but not the table itself).
<space>|left aligned table|
<space>|right aligned table|<space>
I agree that the other task is related. However, it got closed, and there was never really any solution for the table alignment problem.
(I do believe that alignment of text as indicated in the related task should be included directly in DokuWiki. It's such a basic task, trivial to do (wrap block in div that includes text-align: CSS) , and we shouldn't need a plugin for basic text formatting, but that's another story.)
There are many plugins, like the box or divalign plugin which allow to center any type of content.