Im sure there will be plenty of Atrocities which the Germans commit when the war kicks off to make sure the Public is sufficently outraged to eliminate doubt in most minds, especially with Propaganda broadcasts and ministry reenforcing it.
Unless you have a holocaust 2.0, not really. The western public will see it as akin to the propaganda of WWI otherwise, so it won't really work. Even OTL, the holocaust was denied fairly widely early on, despite its magnitude, because of WWI propaganda. In this case, there won't be any holocaust, there will probably be much less severe crimes even than WWI, and the public will simply not buy it. Eric Blair defecting to the Comitern shows what direction the British left will be going, anyway. Unlikely people only slightly more centre then him will SUPPORT a war against it. Granted...Britain could go ultra reactionary.
There won't be a holocaust, there won't be lebensraum, and it is likely at least on the western front, rules of war will be mostly followed. Even assuming say, excessive civilians casualties occur due to bombing, it may not be enough for citizens to wan't to die for, especially if they feel their government dragged them into this crisis.
Its also important to know that the worst regime in this timeline as far as I can tell is the Italian Social Republic, one can look at their attrocities towards Slavs Libyans and Ethiopians OTL to see what the public will be looking at TTL.
This Germany isn't anti semitic by all accounts in the trailers, Hitler will probably still be fairly crazy especially if he retains his meth addiction, but that might manifest itself more into outlandish battle plans he has.
Regardless, America is essentially not going to enter no matter what. Churchill admired Stalin and will still mainly focus on Japan, a capitalist colonial nation ttl Hitler won't really care about. Given Japanese Soviet border clashes, potentially America may end up a co comintern belligerent on the East, though that is perhaps questionable.
If Britain enters the war, the Comitern can steamroll the mideast fairly quick and begin to enter India. Bose, who initially looked to the soviets to free India but got snubbed OTL, will gladly co operate with them in this timeline. It's important to know Indians had no love for the British, and despite Japanese atrocities against their POWs, the Indian public wanted to pardon collaborators upon independence as the collaborators were seen by many as patriots against colonialism and Bose today has a very popular legacy.
Even though Germany may be recovery slightly still by 1936 due to the civil war, it is important to note in 1936 Italy is even MORE unprepared than OTL as well. Especially given they may be tied fighting Ethiopians as well in this. Austro Fascist Regime was infamously unpopular and many Austrians will welcome red Germany.
The odds aren't good for the anti comintern - they will be lucky to even get a stalemate to be honest, a socialist Eurasia seems most likely though.