Narcissa is the first to suggest it, then Avery and some others discuss it after Herbology, and Regulus can't see any reason why not. It's the thing to do to make Mother happy, like getting good grades or being on the Quidditch team. Sirius wouldn't approve but then again Sirius is running with a bad crowd. Him and Mother barely spoke ever since he got sorted into Gryffindor, and she made sure that Regulus followed her example. Of course Regulus would. He's the good son. It's his job to keep up the family name and the legacy of the Blacks. He believes in what Lord Voldemort says. How couldn't he, when everyone around him is so supportive of the man? Apart from Sirius, but if anything Sirius's disapproval is what makes him even more certain.
It takes him much too long to realize that the tattoo was his death sentence.