While there are superficial resemblances between Leftism and Religion, Leftism is in essence anti-Religion; and this can be seen from the fact that Leftism is universal acid, while Religion is universal glue.
Both Leftism and Religion tend to subordinate other functional social systems - so that in a Leftist society (in the modern West) all social institutions become primarily Leftist institutions - so that the civil administration (state bureaucracies), schools, universities, churches, hospitals, the legal system, the military, charities etc increasingly and more-completely trend to have Leftist priorities (feminism, antiracism, diversity, environmentalism etc) as their bottom-line function. The sticker label functions such as education, health, law, military effectiveness etc. recede further and further - and get sacrificed more or less completely to Leftist priorities.
Religion is superficially similar in the sense that in a fully religious state (e.g. the Byzantine Empire, Medieval Europe in the ages of faith, Puritan New England or the Mormon state under Brigham Young) all social functions are subordinated to the Religious imperative, and aimed at Religious Priorities.
But although superficially similar - there is a deep difference. Under Leftism the functional institutions are subverted; under Religion they are organised.
Leftism is like acid, in that it destroys the functionality of all social systems:Leftism dis-integrates. Education substantially ceases to be education, health services cease to promote health, the legal system becomes unjust - not by accident but by its intent and nature.
Of course this is constrained in any actually surviving society, because at some point in the advancing wave of Leftism (the 'march through the institutions'), the acid will have dissolved everything which does necessary and useful work, and which holds the state together - and society will collapse. Collapse is what happens when enough acid is applied for long enough.
But Religion works as a glue to hold together all the social institutions - binds them and keeps them pointing in the same direction: Religion imposes cohesion. The systems are subordinated, inevitably the efficiency and effectiveness of any specific system will be compromised to some extent - but the aim is not to destroy institutions but to harness them to Religious goals.
For example, university professors will be required to profess the Religion (or, at least, not to attack it), doctors will be required to practise within Religious constraints, lawyers will be expected to ignore or even contradict laws if or when they come into conflict with Religious morality.
Glue usually does slow up things, and can even clog things - but the overall imperative of sustaining and promoting Religion means that this is not intended - the society is meant to be Religious and also functional - and as efficient as is compatible with this goal.
This is the big, and crucial difference between Leftism and Religion - a difference as large as that between acid and glue.