Ghost syncs all customer data from Stripe, so this is expected. According to Stripe, you should not use one Stripe account for multiple unrelated businesses:
You must use separate Stripe accounts for projects, websites, or businesses that operate independently from one another.
If you have members who are being charged for some other product or service which is $500/mo - that Stripe account should not be connected to Ghost. It sounds like the support agent you reached at Stripe might not have understood the context.
Creating a new account in Stripe is done in the top left corner of the Dashboard, click on your account name to open the dropdown, then “Create new” — the new account is added pretty much instantly, and you will then have a clean slate to work with.
Unfortunately Stripe Connect does not provide us (as a platform/product) with any data about how or whether a Stripe account is already being used for other types of transactions, so we’re not really able to detect or optimise for this in a useful way