Buttondown Documentation
This is a common and unfortunate problem. The short answer is: email is weird, email inboxes are weird, and there's nothing you or I or anyone can do about it.
Buttondown's Markdown preview is meant to closely resemble an email inbox from a content perspective. Text formatting from Markdown and HTML tags, links, and images all appear as they would to someone opening your newsletter email in their email client. But they will never be able to accurately resemble your subscriber's email inbox from a stylistic perspective.
Our friends over at Litmus have a really useful, detailed answer about why this happens. Read their documentation:
Web-based email clients (such as Outlook.com or Gmail) will certainly perform most the tasks listed above, but they also have a larger, more difficult job. They have to prepare the HTML to be converted into HTML that's safe to show within their own email client's HTML. This is a surprisingly difficult thing to do and most web-based email clients' pre-processors will err on the side of being overly restrictive and removing anything with even the slightest potential to affect the layout of their email client. We'll cover the various mistakes made by these pre-processors a little later, but you should expect this to be the second biggest cause of headaches when designing HTML emails - the first biggest cause is still to be discussed.