Hey there. I've been answering a lot of questions recently and haven't had an answer deleted, however I've noted that they want answers to be indepth. Here is my first serious attempt at an answer.

I'd wager your great grandfather worked on the docks and was thus essential. There is no reason a non-essential worker would not be conscripted, it is possible he worked in another essential industry which was exempt from conscription.

The other thing to consider when you ask your question is the wording of "didn't fight". My own great grandfather did not fight in ww2, but he was in uniform and on guard duty on the home front in Canada. Large numbers of men and women in the military did not see action during world war 2.

Liverpool was THE main port for supplies/materials from North America. The British were conscripted according to the perceived needs of the war effort. The Schedule of Reserved Occupations (1939) made exceptions for people in jobs deemed crucial. The list initially included teacher and boilermakers, to give examples of jobs we might not think of as 'vital'. At the same time 1939 was not yet a total war and the British politicians and generals did not know how things would play out, we must strive to see things from their 1939 perspective. Exceptions were lifted over time as the war and manpower shortages became more serious.

The 1940 Emergency Power Act gave the crown control over all British civilians and everyone in the UK. This does not just include sending men to fight in North Africa but gave the Minister of Labour the power to make any person in the UK to perform any service required in any place.

The biggest examples of these policies related to farmers, women and miners. In the first two examples the governments attempts seem to have succeeded.

Domestic agricultural output increased during the war and the British population actually became healthier despite, or possibly because of, rationing. Women entered the workforce and made an important contribution to the war effort. Both of these are well known and also beyond the scope of your question.

In the mining sector the government did not do so well. Too many miners had joined the army or switched to better paying jobs, for example munitions workers made more than miners. From 1939 to 1942 140,000 miners left the mines. The government ended up conscripting 45,000 men into the mines. Over 40% of people assigned to the mines appealed against the orders. Many people were even jailed for refusing to go down into the mines!

One interesting social factor of these conscription, as well as the evacuation of children from population centres into the city, was to open the eyes of upper and middle class Brits to the mass poverty and poor standard of living of the lower and working classes. These classes would not normally interact with each other in the manner which they did so during the war.

To summarize, there is no reason a non-essential worker would not be conscripted. As Liverpool was the UK's most important port large numbers of young men were needed in order to keep the port running. Your grandfathers profession almost certainly kept him out of the war. I would try and find out what this was.

Source: Charlot, Monica British civilians in the Second world war (1939-1945) 5th Edition 1996 Published by Didier-Erudition PP 128, 137-142

EDIT: Changed federal government to the crown