Itch does support the headers for SharedArrayBuffer, but it causes problems if you want to have both a web player and a downloadable version of the game. It was

Itch does support the headers for SharedArrayBuffer, but it causes problems if you want to have both a web player and a downloadable version of the game. It was recently fixed for Chrome, but in Firefox trying to download a game from a page with SharedArrayBuffer results in the browser blocking the download from the CDN.