Is alcohol-free beer halal?

There is genuinely no single, universally agreed answer to this - it depends which scholarly approach you follow, and we would be doing you a disservice pretending otherwise.

The permissive view: some scholars (a position attributed to Ibn Uthaymeen among others) hold that the test for haram is intoxication, and since a drink at 0.5% ABV or below cannot realistically intoxicate, it is permissible - though some who take this view still recommend avoiding it out of caution.

The stricter view: other scholars and fatwa bodies focus on the production process rather than the final ABV - if a drink is made via the same fermentation route used to make khamr (wine/beer in the intoxicating sense), some hold it remains impermissible regardless of how much alcohol is later removed.

Because this genuinely varies by school of thought and individual scholar, the honest answer is: check the specific certification on the product if it carries one, and if it matters to you, ask your own local imam or trusted scholar rather than relying on a general answer from a drinks review site.