...people not wearing yajnopavita...
This is wrong premise. Dharma and Moksha are independent although dharma secures Moksha. As an analogy any message signal when transmitted over a longer distance it is modulated with career signal because message signal is prone to distortion along the way. So, all these samskArs, varNashram dharma etc are nothing but career signals which are in no way decides moksha, but are traditions which passes the message to the next generation and rest of it. So, the part of casteism is related to dharma not Moksha. Moksha transgresses any border of conditioning, birth, nationality etc.
Are there any examples of them attaining Moksha or Oneness with God(Brahman) or Oneness with their Ishta Devata without being born as Brahmin?
The words GOD or Moksha or Oneness are my pet peeves, nevertheless would say Nisargadatta Maharaja was self realized person who was non-brahmin. He was an Advaitin belonged to nAth Sampradaye. He is very influencial at least according to me. This is what he said
My Guru ordered me to attend to the sense 'I am' and to give attention to nothing else. I just obeyed. I did not follow any particular course of breathing, or meditation, or study of scriptures. Whatever happened, I would turn away my attention from it and remain with the sense 'I am'. It may look too simple, even crude. My only reason for doing it was that my Guru told me so. Yet it worked!
Heis one among many; Lao Tsu, Mansur al haq, Ekhart Tolle etc are other examples. Btw, I found this one quote of him very fascinating.
I am not a woman, I am not a man
neither a saint not a god
I am not the body, I am not the mind
I am not a person of any kind
Neither the self, nor the soul
but much much deeper than the black hole
I am nothing but I am everything
Because everything is nothing and nothing is everything.
But personally I won't recommend you to be Advaitin without any guru from perfect unbroken lineage otherwise you will end up superimposing all the glories of self upon the mind. But if you have Advaitic intuition in the sense you are capable to indwell in the self or say in 'being' than 'becoming' you can start practice although defective it may be.
My Guru told me: "...Go back to that state of pure being, where the ‘I am’ is still in its purity before it got contaminated with ‘I am this’ or ‘I am that.’ Your burden is of false self-identifications—abandon them all." My guru told me, "Trust me, I tell you: you are Divine. Take it as the absolute truth. Your joy is divine, your suffering is divine too. All comes from God. Remember it always. You are God, your will alone is done." I did believe him and soon realized how wonderfully true and accurate were his words. I did not condition my mind by thinking, "I am God, I am wonderful, I am beyond." I simply followed his instruction, which was to focus the mind on pure being, "I am," and stay in it. I used to sit for hours together, with nothing but the "I am" in my mind and soon the peace and joy and deep all-embracing love became my normal state. In it all disappeared—myself, my guru, the life I lived, the world around me. Only peace remained, and unfathomable silence. (I Am That, Dialogue 51, April 16, 1971)
Wait... How could I forget legendary Gautama Buddha!?