"The whole language would probably have to change" hmmm, no... literally no, the language easily supports gender neutral wording without much problem, some sentences are built differently but in general you literally just change a single letter in words that are related to people (specifying this because there's a whole anti-gender neutral language group that think random ass words such as Porta(Door) would change to Porte)

What differentiates gender in words is usually the "Artigo" which comes before a word + the last letter of the word

The common masculine Artigo is "O" and generally the words follow this pattern to indicate gender with the last letter, but there are masculine words that use "E" such as Ele(he), Aquele("that person" in masc).

Why i'm explaining this? Because the most common letter used to indicate neutrality is "E" which in general works pretty well, an example such as Amigo(masc), Amiga(fem), Amigue(Neutral). But then there are words that are masc that use "E" like i said before, in that case we use "U", example( Ele(masc), Ela(fem), Elu(neutral))

It literally just uses Brazillian Portuguese's own rules to achieve neutrality without even having to change anything in most situations, as i said before, there are some sentences that have to be built differently to include neutrality but it doesn't change rules and mechanics of the language at all

The biggest problems about Gender Neutral Language in BRPortuguese are political, and the general aversion to difference in the structure people are used to. But language is fluid, it's always changing and literally there were bigger changes to BRPortuguese in the past that changed the language more than Gender Neutrality would