They're not suggesting getting rid of grammatical genders (which would be entirely impractical). As far as I can tell by the article, this is about teaching forms - that are already in common use - that avoid the problem of gendered language - such as 'Studierende' (the non-gendered progressive form - literally 'those who are studying') instead of the generic masculine plural 'Studenten'. The 'gender star' isn't all that alarming either. It just means you give both the masculine and feminine form separated by an asterisk - 'Student*in'. In speech, you mark it with a short pause. There's no reason why non-native speakers would make fools of themselves using these correctly. I use them, and I'm a non-native speaker (albeit near-native).
Some German broadsheet media get round the problem by alternating generic feminine and masculine forms. That's my preferred method, if it's practical.
(This post is not a comment either way on any of the associated issues - just to point out that Cambridge is not in fact entirely rewriting the language, as the article's headline and initial paragraphs make it seem).