It sounds like you're dealing with an overlay rather than a traditional pop-up, which is why your pop-up blocker isn’t stopping it. Since this doesn’t happen on Chrome, it’s likely a browser-specific setting issue. Many sites like the NYTimes use a cookie or local storage method to remember your agreement, and if your other browser is set to block or clear cookies, the site won’t “remember” that you’ve already accepted the terms. This behavior can also occur if your browser is in private or incognito mode.
I suggest checking your cookie and privacy settings on the affected browser. Make sure that cookies and site data are enabled, at least for the NYTimes domain. You might try clearing your cache and cookies, then reloading the site to see if that resolves the issue. If the problem persists, consider temporarily disabling any privacy extensions that could interfere with cookie storage.