Rivers of Heresy received a score of 69 out of 100 on review aggregator
Metacritic based on five critics' reviews, indicating "generally favorable" reception.
Mojo wrote that "Empire State Bastard make you feel like you've been in a cage fight with
Mike Tyson". James Hickie of
Kerrang! remarked that the album "manages to surprise by bringing out lesser seen sides of its creators", as Vennart "has long showcased a songwriter of craftsmanship and nuance, so it's startling to hear him being so unremittingly brash here. As it is to find Simon, no stranger to moments of righteous indignation in Biffy, letting rip in larger, scarier increments". Andrew Trendell of
NME thought the album "too hard for most
Biffy fans and not pure enough for many
Slayer faithful, but it's its own wonderfully weird wee beast. These are the sharper edges that Neil let out on Biffy's earlier work, but elevated that the pure ultraviolence of Vennart's songwriting and madcap riffery".
The Line of Best Fits Elliot Burr stated that "the mathy and shouty
post-hardcore of Neil's early noughties output turns its intentionally ugly head once again on the aptly dubbed
Rivers of Heresy", which "flourishes when it veers into heady atmospherics". Joe Goggins of
The Skinny described it as "punishingly loud, often furiously paced, and has Neil vocally channeling
Chino Moreno as he flits between screaming and singing. When it works, it's thrilling, especially on the moody 'Moi' and the mercurial, atmospheric 'Sons and Daughters'". ==Track listing==