In his latest post Rob Allen shows a way you can override the default Twig date filter with your own custom Date extension handling.
In one project that I'm working on, I'm using Twig and needed to format a date received from an API. The date string received is of the style "YYYYMMDD", however date produced an unexpected output. [...] This surprised me. Then I thought about it some more and realised that the date filter is treating my date string as a unix timestamp. I investigated and discovered the problem in twig_date_converter.
He includes some example code you'll need to create the custom renderer. As part of the internals of how Twig formats the date currently is internal and can't be changed, he opted to override the extension itself. As a result, the call to the filter is exactly the same as before, the output results are just formatted more correctly.