Why do MPs display a contradictory moral compass over renewal of the Trident nuclear WMD system?

At prime minister's questions on Wednesday (22 May) -possibly Mrs May's final appearance?-  former Labour MP, now disaffected independent John Woodcock- representing Barrow-in Furness, the home of BAE Systems' Trident Submarine shipyard - asked the first question on the alleged use of chemical weapons again by Syria, describing this use as the "indiscriminate evil " of deadly weapons. (https://hansard.parliament.uk/commons/2019-05-22/debates/D0FB8DEF-CF6B-4254-83FE-20CE25D8DB1B/Engagements)

Yet Mr Woodcock is the biggest backer in Parliament of Trident nuclear WMD replacement because of the jobs it supports in his local Barrow shipyard. 

But surely he must be aware that any use of Trident would constitute the most indiscriminate use ever of a WMD. Indeed, the day before PMQs, the United Nations' head of weapons research, Renata Dwan, as director of the UN Institute for Disarmament Research (UNIDIR) said the prospective use of nuclear weapons was "at its highest since the second world war,"  and a called for politicians to take urgent action to address the threat of such a catastrophe.( https://www.reuters.com/article/us-un-nuclear-idUSKCN1SR24H)

How does Mr Woodcock  justify this backing of extending the UK WMD capability another sixty years with its renewal this clear contradiction in his moral compass?

And why does Labour's shadow defence secretary, Nia Griffith,  and many other MPs too, agree with him?