On a philosophical level, do you agree with this idea?

I don’t think they are contradictory statements. It only says that you should consider what others are thinking but need to stick to yourself if that’s the right way to do irrespective of what they will say. It’s about standing your ground only after giving due consideration to other’s perspective.

I do agree with it.
It is wise to explore all angles of an issue, and give other people’s opinions an honest evaluation.
If you are certain you are right, don’t worry about what other people think.

The entire point of having a debate/discussion is defending your position, which in turn automatically makes you care what other people think about your opinions.

I don’t agree with the spelling, for starters. The word intended in both statements is – or should be – others’.

It’s not inherently contradictory, but it could be. For example, if your opinion on an issue becomes “an issue” in itself, that is to say, that it becomes a controversial opinion which rises to the level of “an issue to be discussed”, then it is contradictory. Because in that case others’ opinions on your opinion would be their opinions on “the issue”. But that’s an unusual case which tends to validate the general rule.

On the other hand, there’s no particular reason to be concerned with others’ opinions on issues, either. If you want to be a hard case, then why worry at all about others’ opinions?

It’s stating that your
opinions should not vary with the audience receiving them.

I’m not sure I care about other peoples’ opinions on issues, other to know that they exist.

And I pretty much don’t care what they think of my opinions.

I think it is saying that you should care about what others think…try to learn from their ideas. But don’t let them dictate your own ideas. Live with others but be yourself.