I believe "morality" is objective. ( quotation marks here because it goes by many names )
I wouldn't say it can even be subjective, by definition, as the distinction between right and wrong . It's either there or it isn't. And if it isn't, nothing is ultimately right or wrong, at which point "subjective morality" i.e. personal opinions attempt to separate right and wrong (but why/how, since nothing ultimately is right or wrong). Likewise on the other hand, if something ultimately is right or wrong, then how can it be subjective?
Still, that doesn't prove whether or not morality itself is true. In the case morality is not true, I completely understand why people would repurpose the meaning of it, and conclude that "morality is subjective". However, I am in the belief that morality is true.
Instead of myself trying to explain my observation, I'll refer to C.S. Lewis, who does a fantastic job explaining it.
(While I'm at it let me mention that this is from a series of doodles along old recording of his book Mere Christianity, and I can highly recommend watching the rest as well!! Also for you atheists / non-christians out there as it's not just about Christianity, you might catch some interesting points. He also goes deeply into the subject of WtM and does a very thorough job at it )