People commonly have a preference to 'work on the left' (of the brain) or work on the 'right'. What this means is that there is a natural, biological preference to work in one hemisphere of the brain than the other.

Right or left does not refer to competence but to preference. Those who are capable in one hemisphere are commonly capable in the other - but may not have the confidence to do so.
A left-brain preference implies a desire for predictability, certainty, clarity, and detail. The person is likely to be analytical and needs to be convinced before there is acceptance.

A right-brain preference implies a comfort with the abstract, ambiguous and creative tasks. The person is comfortable in non-exact 'spaces' and works through them without much discomfort.

The implication of this is as follows: the place a person sits within an organisation or the work that the person does for a significant period must sit with their respective brain-hemisphere.

What this means is that although most people can operate in either hemisphere, they struggle to do it over long periods because it’s not their preferred brain activity.

Left-brainers are suited to performing analytical and exacting work over long periods. If as a result of a change initiative, you ask them to be creative over the long-term, or to work under a matrix style management structure, then they will probably stress because they are out of their comfort zone. A Matrix style of management requires a person to answer to multiple managers with differing and sometime competing priorities. A left-brainer needs precision so this ambiguity and imprecision is likely to be stressful.

Right-brainers like to set their own agenda, be responsible for outcomes but not for exacting rules or processes. They value opportunities to be creative or to work on abstract concepts and ideas. They don’t feel much stress during changes in the organisation and go with the flow. They do however, feel uncomfortable with tight control. Therefore, if you were to impose on a right-brainer deeply analytical work with tight controls over long periods, then stress and discontentment would surface.
Interestingly, successful managers can operate in both hemispheres with high competence for considerable periods.

The point here is, you should know the psychological make-up of the people that your organisation is impacting before you decide on solutions and a change management strategy.