I'm kind of confused by this idea. In general, all 1000 players have similar levels right? Yeah people may have different strengths or weaknesses, but "good 1000 player" seems to be rather illogical in the sense that if you are "good" compared to the population 1000 players, you would gain rating and hence no longer be 1000.
Live up to your rating!!

you ever played a 1400 and had hard time to fool him but played a 1500 and it was a piece of cake?
thats what it means. one of those really lives up to his rating and a good player and the other is just an overrated one.

Oh if you are talking about rating accuracy, I'm not sure why it's a big deal to "live up to your rating" because most people want to improve
but also people have off days, like me right now for instance bc i am sleep deprived

It's not exactly about that, just tried to answer your question in a different way.
real point is about what is a good player, rating is number of your accumulated knowledge and experience. but not a measurement of your being good or bad..
if you are on the right way and coming, then you are a good one. do not get demotivated by the people who says you are trash because you are one thousand.
It will just be a matter of time

Oh okay, yes, then I agree with you. Suppose you want to improve, it's far more important that you are playing with good habits that will serve you well in the long run, and maximize your growth whatever your ultimate trajectory looks like.
I think maybe that could be clearer in the OP. I'm really glad someone posted this in the forums; I think it's a super valuable point.
I feel like it's also a growth mindset/fixed mindset type of thing; the person who says XX rating is trash is using more of a fixed mindset that ignores the fact that people's skill is a work in progress depending on the effort they put into it
I just read a post "Is my xx rating good?" i can extend it to "Am i a good player" "I'm rubbish at chess".. some people even think that they are not smart..
this is a wrong way of thinking.
if you are a 1000, your question should be "am I a good 1000 player?" "Do i know opening principles? Common game concepts? How often do İ blunder a piece or a pawn? What do i do to improve it"
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think about a kid in an elementary school, is he or she a good student? who you gonna compare him with? an engineer? no!!
comparison will be between him and his classmates. he doesnt know much (yet) but he works well and he is smart too. and he will definately be someone important. he has a potential. which means he is good.. no matter which class he is in he deserves respect.
same applies to chess and everything. 1000 doesnt mean you are bad. It means you are climbing ladders..
dont listen stereotype naysayers, make a plan and stick to it.. good players act like that.