I haven't had time to click on and follow the debate, but it seems to assume the Germans invade Belgium like OTL. I was somewhat surprise to see it posited that Britain remaining neutral even after the German invasion of Belgium was a real option, though Ferguson in "The Pity of War" seems to favor this position.
There is another long thread that looks at what would have happened if the Germans had not invaded Belgium, and many people have cogent arguments that Britain would have gone to war against Germany anyway, though on the whole opinion seems to be leaning in the other direction.
Thinking about this, it seems the invasion of Belgium is a really big deal, more than I thought. These are the reasons:
1. Germany is now invading a neutral country. There is no invasion of a neutral country otherwise, and otherwise its hard to make the case that they are fighting anything other than a defensive war.
2. The British guarantee of Belgium.
3. Germany takes over major coal producing regions and Germany armies are in Flanders, which is particularly sensitive to Britain. This doesn't happen, and its actually hard to see where the British send the BEF if Flanders isn't a theater of war.
4. Invading Belgium gives the chance of Germany knocking France out of the war early, which was the whole point, and now you get hegemonic Germany. They can't knock France out of the war early by going through the Lorraine fortresses. No invasion of Belgium and France is guaranteed to survive any peace no worse off than they were before, except for the war losses.
5. Seizing the industrial areas and the Belgian nitrate stockpile really helped Germany and without an invasion they don't get these advantages. So they will probably "win" a two year war, given the OTL German and Russian military performance, but we are looking at a two year war, a bigger version of the nineteenth century wars, where the German army performs somewhat worse than OTL and the gains are limited.
From the British perspective, the Germans occupying Belgium makes them a threat. If they don't occupy Belgium, they are not a threat. Its as simple as that. That is why the invasion produced a consensus for war. Otherwise, there were British elites wanting a fight but no consensus and it would make even less sense for them to declare war.
As to my opinion of whether the declaration of war after the invasion by Britain was a good idea given hindsight, I am leaning to the view that they had to do it, but should have fought the war differently, with no continental commitment or conscription and war aims limited to a German withdraw from Belgium and northern France, plus reparations for actual damages. This would have given a chance of a more limited war that the British were better equipped to fight.