Short answer: Not very.
We obviously don't have a database of ongoing valuations for private businesses in the US. We could possibly look at private equity funds, but there are some significant drawbacks to those databases. An alternative proxy is the microcap space. The Russell Microcap index consists of roughly 1,500 companies with a median market capitalization of USD 220mn.
Overall, the microcap index is highly correlated to US equities in general. However, individual companies within the index are not. Of the 1,500 companies in the index, 1,200 or 80% have a correlation to the S&P 500 of 0.5 or less. The median correlation is 0.3. That's pretty low. For perspective, we expect corporate investment grade fixed income to have a correlation of about 0.3 to US equity. A correlation of 0.5 is about the same as emerging markets fixed income and US equity.
Just to be clear, low correlation doesn't mean "not risky." Microcap stocks exhibit very high volatility, which is an indication that although they don't have a lot of market risk, they have a massive amount of idiosyncratic risk, on average. Private businesses and private equity should be viewed the same way.
Generally speaking, private business owners should mentally categorize broad exposure to public equities as a diversifying position instead of one that doubles down on the exposure they have in their private company. In a world where bond investors are looking at returns that are barely above inflation, unnecessarily avoiding equities in favor of what's sometimes called a "muni barbell" removes an important diversifier and source of long-term return from the portfolio.