Short answer: Belgium refused, and Germany invaded anyway
In early August 1914, Germany demanded free passage through Belgium in order to attack France. Belgium refused. Its neutrality had been guaranteed by the major European powers under the 1839 treaties, and the Belgian government argued that giving way would betray both international law and the nation’s honour. Germany invaded on 4 August 1914, and Britain declared war in response. For the armies of that war, see the evolution of German army uniforms and British Army uniform and equipment in World War I.
In the Second World War, Belgium was neutral again, but Germany invaded on 10 May 1940 anyway. So Belgium did not let Germany through in either war. In both cases, German forces crossed Belgian territory regardless of Belgian neutrality.
The 1839 treaty that made Belgium neutral
Belgium’s independence and neutrality were set out in the Treaty of London of 1839, with the guarantee of the major powers behind them. The Belgian government’s 1914 reply refers to these treaties and to their confirmation in 1870. A treaty guarantee gave Belgium a clear legal reason to refuse passage, and it was central to the country’s position.
The 1914 ultimatum and Belgium’s reply
Germany’s demand came as an ultimatum in early August. Belgium’s reply rejected it. The government said that it had always kept its international obligations and would resist any attack by “all the means in their power”. The Belgian forts at Liège then held out for several days, slowing the German advance into Belgium.
What happened in 1940
Belgium had changed course in 1936. King Leopold III announced a policy of neutrality and ended the military alliance with France. In May 1940, Belgium was still neutral, but German forces attacked on 10 May. The Belgian army fought alongside French and British forces before it surrendered on 28 May. The outcome was similar to 1914: German forces crossed Belgium despite its neutrality.
Why the question gets confused
Search results often blur the two wars. “Let Germany through” most often refers to the 1914 ultimatum, which is widely discussed. The 1940 invasion had different causes and a different course, so check the date in any source before drawing a conclusion about Belgian policy.
What this means for uniform collectors
Belgian soldiers in 1914 and in 1940 wore different clothing. A Belgian item needs dating before its context can be understood. Belgian WWII uniforms covers the 1940 side in more detail, and French WWII uniforms covers the forces that fought alongside Belgium in May 1940.