This stranger talked to me. Usually, I would have had to think something bad would happen. But I followed him.
(One Day in NY) BY Pat Mathew
What is this "would have had to"?
"Have to" can express different levels and types of urgency. In most cases it means must, however it can also have the force of a more abstract "have no alternative but to..." "can't help but..." as in your example.
In the present one could say:
If my husband calls on the emergency line, I have to assume something is wrong.
In the past:
Last week, when my husband called me on the emergency line, I had to assume something was wrong.
In the past, when my husband has called me on the emergency line, I've had to assume that something was wrong.
General, referring to the past:
Back then, under normal circumstances, if my husband ever called me on the emergency line we kept, I would have had to assume that something was wrong.
This same usage applies to your example with "think." The speaker is referring to the way he used to think, how he invariably reacted to a stranger addressing him. In this case "would have had to think" expresses that this would have been his usual reaction (which he makes clear with "usually").
Usually, I would have had to think something bad would happen.
Is a conditional forced action ("have had") in the past tense. In this case a thought of a bad thing occuring under normal circumstances.
In this case:
But I followed him
you can assume that he does not believe something bad will happen, however, something is not not quite "normal" since "Usually" he would be forced to have that thought, but not this time.