Iam64 What Livingstone apparently said was:
"If your local MP is undermining Jeremy Corbyn, opposing the policies, the anti-austerity measures, that we want, people should have a right to say "I'd like to have an MP that reflects my views". It shouldn't be a job for life."
If local Labour Party members are happy with their MP they are unlikely to want to de-select. But if their MP is not that effective and is also continually undermining and ridiculing the policies of a leadership that received overwhelming support, it is surely understandable that if the majority of members are unhappy with an MP's public performance, they may eventually lose patience.
It isn't unknown for local Conservative activists to de-select MPs - Tim Yeo for instance. Yeo suggested his "moderate" views - his support of gay marriage, tackling climate change and staying in the EU - were to blame for his deselection. It's possible that the principal reason for getting rid of him was his ineffectiveness but the addition of views that his local party did not support was unlikely to have helped. At around the same time Anne McIntosh was rejected by activists in Thirsk and Malton. I don't recall there being much of an outcry about either of these de-selections at the time or a suggestion that they were unjust.