Huh?
Many people hold both bonds and stocks and other assets, like real estate.
Index funds give you broad diversification at low fees. That diversification mostly removes out company-specific idiosyncratic risk, but it still leaves you exposed to market risk, and no one in their right mind claims otherwise.
Even a risk averse person (and even more a risk neutral person) can rationally hold on to very risky assets. Risk aversion just means that you require a higher return for a given level of risk.
And a risk neutral person doesn't care at all about risk, they only care about expected returns. That's mostly a convenient abstraction like the famous home economicus.
I don't understand why a risk neutral person would want to prefer bonds and cash?