In other words,
With complementizer The reason that I prefer not to take a full schedule of courses is not because I am unmotivated, lazy, or afraid of work.
Without complementizer The reason ... I prefer not to take a full schedule of courses is not because I am unmotivated, lazy, or afraid of work.
The clause
that I prefer ... is short for
The reason that I prefer ... . If you keep the head noun,
The reason, then you can omit
that, but if you omit the head noun,
The reason, the resulting clause is still remains dependent and so
that is necessary. Which is why
that is important in the second example here:
The reason (that) I prefer not to ... is not because I am ... afraid of work.
That I prefer not to ... is not because I am ... afraid of work.
I prefer not to ... is not because I am ... afraid of work.
Now, the example you have, shown here below, has the pronoun
It for a subject, and that pronoun is anticipatory and has a referent, notably the elliptical noun phrase
the reason: With complemtizer It is not because I am ... afraid of work
(the reason) that I prefer not to ...
Omit the complemetizer
that and the reader/listener will interpret the resulting clause as an independent clause. Which is why this one is ungrammatical:
Without complementizer It is not because I am ... afraid of work
I prefer not to ...
In short, the reason that can't be omitted in your example sentence is because it tells the reader/listener that the clause it heads is dependent.
Does that help?