I vote that Britain gets involved. Part of the math is that it seemed certain France and Russia would win, the British did not want left out of the post-war spoils or redrawing of influences or maps. The more I delve into it the more difficult I find British "neutrality."
That said I think the more compelling and complicated alternative is "what next?"
First, I assume that no invasion of Belgium is a German strategic shift to defend West, attack East, likely based on a more sober minded read of both military and diplomatic reality. I truly feel Moltke was gambling hoping to set his name among the stars. This Moltke sees all the advantages in holding the French until they break and using maneuver in the East to gain victory. While I doubt it is war winning, it sets up a very different war. My assumption is a more even split of forces, 4 Armies worth West, 4 to the East. As an aside Hindenburg likely does not become quite the poster child of victory here, and might get a tough assignment in the West to stiffen the defenses.
Second I assume the British need a little more time to get Parliament to act so the British war machine loses some time, but I think we are counting days or weeks, not more. The BEF deploys and Britain rely upon the blockade more. Blockade takes years and here should be leaky. The BEF is professional and capable but small. With a stalemate at the frontiers the French need to look at Belgium as the way to end the war with Germany. While I doubt the British invade Belgium, I think they regard the Treaty as a "scrap of paper" and give France a pass, holding the right somewhere opposite Luxembourg or the northern Franco-German border. Best case the French go full strength thrust though Luxembourg and tease through Belgium, worst case they hit Belgium hard to strike through to the Ruhr, that will destroy the illusion this is a "just" war. One can see the migration of butterflies.
Third, I think as the war drags past 1914 the British public face some serious disillusionment. That is to me the real effect of this scenario. Any rationale for joining the war now feels paper thin, "free Luxembourg" would be less compelling than "rescue Belgium", the French and Russians look more clearly aggressor and not victim, the Germans gain much propaganda grist, and the blood and bodies flowing out of France make a call for even deeper sacrifices, especially conscription a harder sell. Britain has likely mortgaged itself enough to be dubious of further treasure spent, the French are less desperate and less dependent on the British so they steer an uncomfortably independent course. The Russians still soak up a ton of money and British industry plays a bigger part in supplying them. British industry likely likes this war and the profits. What once looked like a jolly curb stomping of the dreaded Germans and victory parade at Christmas has become the real threat they will win and dictate terms to us after the next mass slaughter near some quaint town in France! 1915 to 1916 become the pivot when Britain needs to either get fully in this war to win or look at graceful ways to exit.
One might still see a big naval battle everyone loves. It might be more about Britain seeking a true victory and it might go horribly wrong. Italy may take the gifts and accept the seduction but stay neutral. Romania might not feel as confident in slipping into this grinder. The Ottomans might have merely gone to war with Russia making it more complex as to how the Anglo-French react. And without the forward bases the German submarine campaign may be a false start. The USA likely sells more to the CP and now has different axes to grind as the blockade hits American commerce. Does America defy the blockade? Russia gets more savaged by German tactical prowess and falters sooner? On and on one finds tattered threads in the unraveled tapestry here to feed butterflies endlessly.
Belgium alone does not butterfly the British entry to war but it sets loose many butterflies over its effort. That is what I ponder over.