Commensalism is compatible with parliamentary democracy.
Commensalism is an economic system in the same way as capitalism is. But where capitalism operates within a legal framework that guarantees the right to economic inequality, that is, the power of the individual to accumulate a more significant part of the entire whole than others, commensalism works within a law that guarantees equality on an economic level. Commensalism proposes we all have equal value, regardless of our differences, and that private wealth thus in principle is prohibited.
But just as different ideologies and political approaches can shape society under capitalism, so commensalism work the same way. It says nothing about how to design social functions. How extensive the collective functions should be, which laws to write, which investments to make, which behaviours to promote and which to oppose. There is room for highly diversified policies within a commensal paradigm.
Representative democracy is probably the most rational collective governance method, at least for large groups. But common control is not always the most effective, and it is one of the reasons why commensalism, unlike socialism, allows private ownership in the form of decision-making in your own company. Private property in a commensal system does not include the right to the surplus value from work performed within the framework of companies, but it gives the owner the power to make executive decisions.
In a capitalist system with significant differences in income, it is necessary for the state to guarantee access to health, education, housing, a minimum standard of living, etc., also for those with small resources, for society not to collapse. In a system where everyone has more or less the same economic opportunities, this is not as precarious. The state then only has to take responsibility for this when the market fails to deliver good enough products and services - because in so far as the market can do this, these are then also economically available to the entire population. The balance between collective and private suppliers and producers is up to the political will at all times.
People like to vote. They do not wish to decide and understand everything. Most want democratically elected representatives to speak on their behalf. Commensalism is not a workers' rule that abolishes ownership as a means of income and placing all power in governmental or collective positions. It is introduced through a radical decision to distribute the corporate profit of society equally among the entire population. It removes labour as a commodity on the market, but it is also the only thing it does. Beyond that, it's business as usual. There will be significant differences in the lifestyle of the rich and the poor, but for the largest group in the middle, there will be no significant practical change. For the oppressed, life becomes more comfortable, but also the large group will gain because they no longer have to live with the knowledge that their prosperity is at the expense of others. The only ones who have something to lose on such a change are those who are already considerably wealthier than the majority.
But introducing commensalism with the help of parliamentary democracy is another issue. In principle, it is possible, but in practice it becomes tough. Resistance from capital forces will be massive, and access to capital means the power to influence. Although most would benefit from a commensal system, capital owners would never voluntarily give up control and privileges.