BARTER VS. MONEY
Barter and money are both ways of exchanging things on the basis of "equal value for equal value." In contrast to both barter exchange and money exchange, the basis for exchanging things in an egalitarian sharing economy is NOT "equal value for equal value" but something very different: "From each according to reasonable ability, to each according to need or reasonable desire with scarce things equitably rationed according to need."
In an egalitarian society, however, membership in the sharing economy (click here to read about what that is) is voluntary. If a person (or family or group of people, but from now on we'll only speak of a single person) wishes not to be in the sharing economy then that person is free to opt out of it. In this case the person is also allowed to own as much of the means of production (land, equipment, etc.) as he/she is able to productively use by his/herself without any hired (or slave!) labor.
Such a person is also free to barter the fruits of their labor with other individuals or economic enterprises that may be either in or not in the sharing economy. But there is no money in an egalitarian society.
WOULDN'T MONEY INEVITABLY ARISE IF THERE IS BARTER?
It is true that when barter is being used to exchange things then IOUs could easily start to be used to barter, say, a future crop for an already-existing product or service. Mary might give Jose an IOU, for example, that said, "Mary promises to give Jose 10 bushels of corn next year in exchange for Jose's having given Mary a winter jacket this year." But this IOU is not money. To be money it would have to say something like, "Mary owes the bearer of this IOU X dollars."
To be money an IOU would, in other words, a) have to be transferable to a third person ("the bearer of this IOU") who is not Jose, a person who in turn could transfer it to yet another person and so on, and b) have to express the debt not as something concrete (in this example "10 bushels of corn next year") but rather in terms of a unit of money (e.g., "X dollars.")
The transferability of an IOU debt, and the expression of the debt as some amount of units of something (such as dollars) the only real usefulness of which is to exchange for a concrete product or service, as opposed to an actual concrete product or service, is what enables money to play the terrible role in society that is discussed here. This is what enables a single person to acquire a virtually unlimited amount of wealth and hence power. Money, unlike mere barter IOUs, can be concentrated without limit in the hands of a single person.
An egalitarian society would make the issuance of money (including any IOU that had the special features of money as described above) illegal.
It may very well be the case that some people would want to issue money-IOUs, just as it may very well be the case that some people would want to hire employees for a wage payment (which would of course require the use of money). But just because some people want to do something doesn't mean that egalitarians are required to let them do it. Hiring wage workers and creating money are simply not allowed in an egalitarian society. Were these things allowed it would be only a matter of time before class inequality would re-emerge as terrible as what we have today.