Currently, according to What are the exact criteria for the "new contributor" indicator to be shown?, the new contributor indicator is enabled by default on all sites, except Stack Overflow for Teams and Enterprise.
I request that it also be disabled on sites that are in private beta. This is because the only people participating on a private beta site are those who committed to the Area 51 proposal or accessed the site from the link on the proposal.
Also, by definition, everyone is a new contributor on a private beta site, because the site was just established. According to the current rules for displaying the indicator, everyone participating in the site would get the indicator on their own posts.
Therefore, it doesn't make much sense to display the indicator on sites that are in private beta.