The relevant feature of the rakshasa is the following (emphasis mine)
Limited magic immunity. The rakshasa can not be affected or detected by spells of level 6 or less unless Wish to be. It has the advantage of saving shots against all other spells and magic effects. (Monster manual, P. 257)
As booming leaf is a cantrip, and cantrips are spells of sixth level or lower, the rakshasa can only be affected by the booming leaf Cantrip if you wish, as indicated by the quotation and the emphasis above.