How your brain's frontal lobe is involved in dreaming
Most evidence appears to show that frontal lobe activity decreases during bot REM sleep (Rapid Eye Movement sleep, where most dreams occur) and non-REM sleep (characterized as deeper sleep, with fewer dreams).  This deactivation has been shown by neuroimaging studies such as PET scans, and lower EEG (electroencephalogram) electrical activity specifically characterized by the onset of theta or delta waves.
However, there is alternative evidence which suggests that frontal lobe activity increases during REM sleep. Research shows that the medial pre-frontal cortex (PFC) activity increases during sleep, but dorsolateral PFC activity decreases when sleeping. They go on to say that the frontal lobe reactivates during sleep, which may be the cause for hallucinatory dreaming experiences.
There is evidence to suggest that the frontal lobe contributes to uninhibited dreams. Activation of the frontal lobe has shown to increase vivid dreams and even nightmares in patients. Furthermore, 80% of patients who underwent a frontal lobotomy (i.e, damage to the frontal lobe) reported no mental activity during sleep. Studies have also found a correlation between frontal lobe deactivation and the reporting of dreams
I also encountered a supportive theory on this in one of the neuroscience novels I have read. The author supported a similar notion, stating that one’s uninhibited activity is a consequence of decreased frontal brain activity that would otherwise prevent you from thinking or acting out such dreams in reality. This reiterates current research indicating that frontal lobe deactivation may contribute to your shyness/lack of conscience.
This idea indeed does have face validity, as the frontal lobe is known to be largely responsible for planning, impulse control, and decision-making. Thus, lowered FL activity would decrease one’s self-consciousness, yielding reduced shyness.
However, this it not to say that it is a pure 1:1 relationship between the frontal lobe and uninhibited dreams. Frontal lobe damage has not lead to a loss in dream formation, but parietal lobe lesions stopped all dreams entirely.Evidently, there are more brain regions involved in the act of vivid dreaming, such as the visual cortex. Moreover, alternative research has evidenced that increased frontal lobe activation leads to increased dream recall, which counters previous data.
Thus, although there is strong evidence to suggest that yes, FL activity decreases during sleep and that this may contribute to your shyness/lack of conscience while dreaming, we also cannot ignore contrasting evidence.