You're right that the common sentiment is false. People will say that subjectivism or relativism is true and use it as a ground for saying that you should tolerate every perspective. That simply doesn't follow. But the reason why it doesn't follow is instructive, because I think it does show why one thing you're saying is wrong while revealing a different problem.

You say it's inconsistent to say that someone should do something while maintaining relativism, but that's not true. If subjectivism is true, then I can say whatever I want. Some varieties of relativism have different ways of determining whether my statements are true, but subjectivism says it's true if I really believe it. If I think you should be tolerant, then subjectivism says that within my perspective you should. Since my perspective is what makes my statements true or false, then that statement in my mouth is true. It's not inconsistent. It's a automatically true.

The deeper problem, though, comes when you consider what's true for the person hearing it. The statement was true when the person uttered it, but the person hearing it may well hear a question that's false, and the person may have no obligation whatsoever to do it. That means a true statement about someone's moral obligation (from the perspective of the speaker) is false (from the perspective of the hearer). It makes communication about moral matters perfectly useless.

Other kinds of relativism aren't like this. One relativistic view is that what makes something right or wrong depends on what's in the self-interest of the person doing the action. If it's in my self-interest to lie but not in your interest for you to lie, then lying is right for me but wrong for you. So right and wrong will vary from person to person, but statements about what's right for person X won't vary in truth value from person to person the way they do with subjectivism. If you told me it's wrong for me to lie, you'd simply be wrong according to this view. That weird feature of subjectivism that doesn't allow moral conversations isn't going to be present in every kind of relativism.
 

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If subjectivism is true, then yes you can say whatever, and it is true. But that does not make it rational.

I could say 'I think I am a poached egg', and the statement could be true (I could indeed think I am a poached egg). But the statement itself is irrational nonsense, because poached eggs do not think.

Note that I do not think the statement is irrational due to it referring to something that is untrue (As in, it is untrue that I am a poached egg), but instead it is nonsense because it treats different categories of things as related. Poached eggs and thinking.

As another aside, morality implies an obligation. If this is so, then subjectivism has more problems because it seems to say that I am obliged to do what I think I am obliged to do. But what am I obliged to do what I think I am obliged to do? An infinite recursion results.