The first link of paṭiccasamuppāda is “avijjā paccayā saṅkhārā” (conditioned by ignorance, formations arise). Analyzing this from the perspective of the Abhidhamma:
Ignorance is moha concomitant with the 12 akusala cittas
Formations is cetanā (volition) in the 12 akusala cittas, cetanā in the 8 kāmāvacara kusala cittas, cetanā in the 5 rūpavacara kusala cittas and cetanā in the 5 arūpavacara kusala cittas (these are the kamma that have the potential to create rebirth, both unwholesome kamma and wholesome kamma)
The second link of paṭiccasamuppāda is “saṅkhārā paccayā viññāṇaṃ” (conditioned by formations, consciousness arise). Analyzing this from the perspective of the Abhidhamma:
Formations are defined as part of the first link
Consciousness is the 32 lokiya vipāka cittas (sense-consciousness, receiving, investigating and all the life-continuum cittas); does not include the kamma-creating cittas, the supramundane cittas or the functional cittas
So your assumption that "all mundane consciousness regardless whether they are wholesome or unwholesome in root occur with ignorance as a condition" is not correct.
You are correct that birth is dependent on the existence clinging and the desire of being (due to ignorance). However, this does not imply that the specific kamma-creating citta which generates rebirth into an existence contains a root of ignorance. If this were true, then there could only be rebirth in the Woeful Planes.
The fetters, the things that bind one to saṃsāra are latent and do not arise in every citta.
Rebirth-consciousness is a life-continuum citta. Jhānic states are kamma-creating cittas (not life-continuum).
@Amansa, you seem to be conflating things from the macro-view (paṭiccasamuppāda) with things from the microscopic-view (Abhidhamma) and this may be the source of your confusion. I suggest that you start with reading the Comprehensive Manual of Abhidhamma (page 295 - 298 analyze paṭiccasamuppāda).
Follow on Answer
What causes rebirth with three wholesome roots? Superior three-rooted wholesome kamma (See page 214 of Comprehensive Manual of Abhidhamma). Three-rooted wholesome kamma arises when a wholesome intention arises together with understanding. Superior means supported before and after by other wholesome kamma.
If I offer food to a monk, that is wholesome. If I offer food with an understanding that this is a meritorious deed, then this is three-rooted. If I offer food reluctantly, or regret later, then this is inferior (not qualifying as superior). If I rejoice before and after the offering and the offering is done with understanding then superior three-rooted wholesome kamma is created.
If this superior three-rooted wholesome kamma plays the role of rebirth-linking at the end of my existence, then the next life will have a life-continuum citta containing three wholesome roots (maybe human, perhaps even deva). A being whose life-continuum citta has three roots has the potential to attain jhāna and sainthood. A being whose life-continuum citta does lacks three roots cannot attain jhāna or sainthood in that lifetime.
Having a life-continuum with three roots is a minimum requirement for jhāna and sainthood. Actually attaining jhāna requires developing the accumulations to temporarily supress the five hindrances. Actually attaining sainthood requires developing the accumulations of the pārami.
In my opinion, a being whose life-continuum citta has three roots is likely to be “spiritually inclined”. In other words, they want to develop the accumulations. In my opinion, a being whose life-continuum citta does lacks three roots is unlikely to be “spiritually inclined”, more likely to be hedonistic, so they don’t have the motivation to develop accumulations.
I believe that there are many, many humans whose life-continuum citta has three roots. Based on the fact that you are asking these questions, I suspect that your life-continuum citta has three roots. But having a life-continuum citta with three roots is only the starting point. Spiritual development is necessary to build accumulations for jhāna or sainthood (and this takes a lot of training).