The rift dates to WW1, not the 1930s, and considering the three arrows to be a better marking of the rift than the SPD literally giving the order to murder KPD is nonsensical.
There was no split in 1903 - the SPD simply had both a revolutionary and electoral faction.
And Bernsteinian revisionism wasn't about taking power through elections or through revolution (which is what the SPD took position on in 1903), it was about the idea that capitalism wasn't going to implode on its own and that accelerationism was a bad policy (on which he was objectively right), but he still allied with revolutionary Marxists such as Liebknecht in the USPD.
Why the USPD? Because he was essentially excluded from the SPD for not supporting WW1.
Hence the doctrine of social fascism - the SPD supported war (and to some degree imperialism), so the KPD and the USPD exaggerated this and called them fascists. That was a result of the core reason of the split, which is differing views on war.
The split itself was already an abyss in 1920, it did not in any way get worse - indeed there is little that is worse than armed confrontation.
There was absolutely room for united forces is the SPD didn't kick out the KPD and USPD (including Bernstein) over WW1, and then progressively gotten more and more centrist as predictably the pro-war position was beneficial to centrists. Without that central event there would have been so split. The USPD is an example that shows that both revolutionary communists and social democrats (by the definition of the time, you would call them communists nowadays) were able to work together as they all agreed that electoralism and harm reduction were inherently necessary, that capitalism had to be abolished, and that this abolition had to be done fairly gradually.