The petition only makes legal sense if it were to ask to extend the set of charitable goals as specified in the Abgabenordnung, but the existing set already allows for FOSS projects as part of e.g. the "national education" category (public code is educative).
And, to be frank, I also don't get the "recognition" part. The tangible benefits of volunteering for a charity are limited; what does it even mean to get recognition for it.
It may be educative but that is hardly the most significant way in which open source code is beneficial to society.
Dependent on the project, other categories might work too. The list is in Abgabenordnung §52 ( https://www.gesetze-im-internet.de/ao_1977/__52.html ) / Fiscal Code Section 52 Public benefit purposes ( https://www.gesetze-im-internet.de/englisch_ao/englisch_ao.p... )
(Contrary to intuition, "advancement of science and research" is very hard to get accepted in unless you're a university or at least publish papers in journals. And while the law claims that in theory other purposes could be argued for, in practice tax authorities will simply stick to the list and not make exceptions.)