The complementiser that is the first word in a complement of a noun♦. When can it be omitted?
Do 1 and 2 below differ?
I am asking in general, but I exemplify with Prof John Lawler's examples modified by me:
1. He concealed the reason that he had robed.
2. He concealed the reason he had robed.
Please exclude and omit reason why, about which I ask not because 'why' is redundant.
♦See [5][vi], p 176, A Student's Introduction to English Grammar (2005) by Huddleston, Pullum.
Best Answer
Rule of thumb: You can always omit that after the reason (i.e. the reason (that)). Put it another way, wherever you can say the reason that, you can omit that.
That vs. Why: You can use that (which is optional) in place of why but only in defining clauses, and make sure that you use reason not reasons (plural) if you want to use a that-clause. (See Cambridge Dictionary Online's note below.)
Answer: There is no difference in meaning whatsoever.
References†:
Macmillan lists these uses of reason, among others:
Cambridge Dictionary Online lists reason why, reason that, and reason + to-infinitive.
Longman English Grammar (by L. G. Alexander) mentions reason why, reason for which, and reason that shortly.
†Even though you've asked specifically for the exclusion of reason why, I decide to keep all alternatives--reason why, reason that, reason for, reason for doing something, reason to do something--in the above quoted texts, because it could, I believe, make this question more useful for the future reader.