regardless of whether.
This is the idiomatic phrasing, not “regardless whether”* — e.g.:
o “When he wanted to send troops to help end the civil war a year ago, President Clinton told a skeptical public and Congress that they would be withdrawn in December 1996 regardless whether [read 'regardless of whether'] peace had been achieved.” “Bosnia Mission Is Not Justified,” Fla. Times-Union, 21 Nov. 1996, at A10.
o “One proposal . . . would require the companies to pay $6 billion a year, indefinitely, to compensate tobacco farmers — regardless whether or not [read 'regardless of whether'] their crop is needed.” “The Farmers’ Cut,” Courier-J. (Louisville), 22 June 1997, at D2.
Language-Change Index — “regardless whether”* for “regardless of whether”: Stage 2.
*Invariably inferior forms.
Quotation of the Day: “It is true that there are rules of grammar and syntax, just as in music there are rules of harmony and counterpoint. But one can no more write good English than one can compose good music, merely by keeping the rules. On the whole they are aids to writing intelligibly, for they are in the main no more than the distillation of successful experiments made by writers of English through the centuries in how best to handle words so as to make a writer’s meaning plain.” Sir Ernest Gowers, The Complete Plain Words 11 (1954; repr. 1964).