The problem Rin faced in her previous triangle relationship is that the other two girls didn't really get along and didn't even like each other. It's impossible to have a poly triangle with two girlfriends when one of them says about the other: "Shiho-sempai... I hate her!" That relationship was doomed from the beginning.
In this case, however, every one of the three girls likes and cares deeply about the other two. That's a good start to make the poly triangle work.
(By the way, Luminous=Blue sure could have used a few kisses like the one Rin gave Mayuki. Or a lot of such kisses. Just sayin'. )