Using that the logic, many poor people do not taxes in fact they receive net income redistributions from the government for doing nothing but existing and being poor. So, does that mean, they are stealing public services?

A more honest way to view taxes is society elects representatives to determine how to allocate the cost of government to citizens based on some abstract ideas of "fairness" and the "ability to pay" (it may be fair to charge the poor for services, they can't afford, but if they can't afford to pay, why bother?). Included in these costs is the cost of the social safety net for those that are disabled and cannot take care of themselves or experience temporary hardship.

But progressive liberals view government roll differently and see government as doing more than allocating the cost of government but as an alternative economic system reallocating resource among its citizens based on a combination of the "concept of fairness" and coercive "power"... if anyone but government tries to do this, it is called stealing. But in government it is called "buying votes".