These conflicts are irreconcilable because it is the nature of the relationship. This is the concept of "class war". It is inherently violent.
People who are pro capitalist are not on the left.
They might be liberals. Liberalism is not a left wing project.
Far from being no-true leftists, there are many millions of leftists globally. Every one of them works in their way for the abolition of capital.
Whether you agree with the ideas or not is no issue here. The question is where they are characteristics of the Left. If you disagree with the ideas, you are not on the left.