I wonder why King Felipe VI did away with the inauguration mass. While it is true that Roman Catholicism ceased to be the official state religion in 1978, I don't see why, as a privately Catholic King, he would not want to have a mass in Yhanksgiving for his accession. I don't see either how that would be different for example from his having a wedding mass or, I imagine, a funeral mass.
Keep in mind that, while the constitution says that: " No religion shall have a state character", it still nonetheless also says that: "The public powers shall take into account the religious beliefs of Spanish society and maintain the appropriate relations of cooperation, with the Catholic Church and other denominations".