Yes, that's exactly how morality works. People value whatever they want.
No, they don't.
Let's take a look at other systems of rules we've created.
Look at a clock. Whatever time it is, let's say 11:23am. Is it objectively 11:23am?
Well, in the confines of the universe it isn't, but within the shared system of time, it is. If you say, we'll, I have my own time and it's not 11:23am or if I told you it was 11:23am and you told me that was just my opinion...Is it just my opinion?
You can say it is, but I bet you don't live by that.
Try showing up to an interview 1/2 hour late and then telling your potential employer that time is subjective and a matter of personal opinion and see if you get the job.
Point is, the system of rules we create is subjective in a sense, but in practice, we all understand these systems and abide by them, not because of their subjective or objective nature, rather because they have value to enough of us and that makes them useful.
It is our desire to accomplish things and avoid others that relate to our shared values that makes these systems useful and morality is no different.
There is no such thing as "personal time, personal measurement or personal morality. I mean, we can all consider other systems of time, measurement and morality, but we always do so in the context of other people with whom we'll share these ideas.