Sony are known for having a strict refund policy and it takes something special for them to let a refund go through. It appears that Anthem could be somewhat special, as several users have reported successful refunds on PlayStation 4.
Sony will not refund games for PlayStation 4 most of the time and chances of it happening at all are slim. No Man's Sky along with its terrible state at launch turned out to be a rare exception as some players managed to get refunds, provided their purchase was digital.
Anthem seems to be pushing this one step further as the game is reportedly crashing the console entirely. This is a hazard that can damage PlayStation 4 units and it appears this could be a reason why Sony are willing to give refunds to those who purchased Anthem in its digital form.
One Redditor initially reported it took them just five minutes to get a refund which prompted confused reactions from other players who know Sony usually don't just hand these out. Another person apparently tested this and found out their refund went through without any fuss.
Soon after, other players started reporting they couldn't get a refund anymore, which points to a possibility that Sony had a surge of refund requests which would cause them to backtrack on the refund approvals.
A similar situation occurred with No Man's Sky after a user talked to an agent and stated the game was falsely advertised. Sony issued a refund as a "one-time gesture of goodwill" which initially worked for some, but players soon started reporting they were unable to refund the game any longer.
If you happen to be a PlayStation 4 Anthem player who might want to refund but was denied for the moment or has experienced a hard crash where you had to unplug the console entirely, it might be wise not to boot up the game until BioWare resolve this issue as it could cause permanent damage to your console.