But founding their first city later means a later start on building a Holy Site, and nowhere to stash a found relic until the city is settled.
You lose the relic option true, but you're not building a holy site on turn 1. As long as you settle a city before researching Astrology, you're not in any worse shape. I think it's still up for debate whether you are more likely to find a natural wonder or not, although you do have a little more freedom to find a site that better fits a holy site by delaying settling. But getting the extra production from forests/jungle could help build them a little faster, and certainly getting faith from features if you have a theatre square helps the faith output.