I half agree with the first point, and agree with the second point, as the second point was what I was putting forth as a requirement in the first place.
Regarding the first, well, you missed my point, due to my failure to eleborate.
Of course, there will be a difference as you say. However, the leading clique of Labour Aristocracy (union bosses) and middle class Marxist intellectuals will still have much the same ideology.
Whilst you are correct in part and I did mention that trade unionists would be in such a party, to say that the vast majority of union bosses would have been completely enamoured of a Marxist party
Take say World War One, the Labour party sided with Britain, this Social Democratic Party, much in line with the Second International will do much the same, for the same or similar reasons. Essentially, you'll have a Fabian party.
But you're guessing that a First World War even happens when we've already established that the POD is thirty years prior to the war's beginning. That's butterfly genocide - no two ways about it.
But, even if we were to accept the premise that all history will have aligned as OTL in the late Victorian and Edwardian eras, then you must understand that social democratic parties held various positions on the First World War within themselves and any current could well have won out given the right prerequisite conditions. Given that this SDP would be a party made up more of Marxists than trade unionists (a largely anti-war group versus a broadly pro-war group, respectively), the emphasis would have been more on opposing any great European war because of imperialism rather than conceding pacifism to the wave of populist patriotism (a wave, I might add, that was fractured and hardly uniform in every household across Britain). If a more pro-war grouping of socialists were to win out, then that would be quite reasonable - but, to say that a party with thirty years of alternate development behind it would go along as per OTL is actually ignoring the myriad opportunities of divergence we are afforded.
You have to remember, and I simplify greatly here, the Bolsheviks were a reaction to Social Democracy. Yes things will be different, things will butterfly... But you will still get a far left trend opposed to Social Democracy whether it be the Bolsheviks or not.
I'm not saying that there wouldn't be a split - when and where and how are all different matters, which is also why it must be clear that your characterisation of the Bolsheviks is a massive simplification (and you rightly pointed it out as such). A trend opposed to a moderating 'social democracy' (remember: social democracy was the term including all socialist currents during the late 19th century and early 20th century) has a high probability of appearing and I've certainly never said that it couldn't, but those kinds of details are best left to the eventual writer of such a timeline who would better grasp their TL's politics (you'd hope, at any rate).