Hi DaneilR,
In Advaita there are two realities: Absolute reality and relative reality. Relative reality is illusory in terms of Absolute reality, so if we speak absolutely, then nothing within reality re ishvara, jiva, world exists. So an Advaitin who only accepts the real existence of the absolute reality treats ishva, jiva and world as practical realities. In the same for example we know Newtonian mechanics is actually wrong, but it serves a practical reality so we still use it in applications of everyday mechanics. Now, as long as you are Jiva, you will indeed experience the duality of ishvara and the world and you will indeed experience reincarnation as well. Some Advaitins make a concession to the relative reality by worshiping Ishvara for instance, despite the fact this is against our doctrine and even Krishna says not to worship his unmanfiest form or the Upanishads tell us not to worship the unmanifest. Worshiping Ishvara(Hiryangarbha) or cosmic intelligence is like worshiping your computer. Pure Advaitins do not worship Ishvara and do not believe in real existence of Jiva, free will and reincarnation. Pure Advaitins practice Jnana to end the illusion of relativity reality and attain liberation.
Have you noticed how some people claiming to be Advaitin start defending Ishvara worship and idol worship and literally become obsessed with it? They cease practicing Jnana and start practicing bhakti to ishvara.
Reincarnation breeds an attitude of complacency, "Nevermind, I will do it in my next lifetime" this creates lazy habits in your mind and basically you keep on going round and round the wheel of samsara. This is why the concept of reincarnation can be a hindrance, you must start your practice now, you must have a burning desire for liberation and put all your efforts towards liberation. It is possible to attain enlightenment in a single lifetime for the sincere seeker.
