It depends. Most HTML e-mail can be parsed within the mutt viewer using an external program that converts HTML -> text in a graceful way. That works for 99 % of the HTML e-mail (which is typically just people that send it that way because they don't know better.)

For newsletters and such, you can have a shortcut that opens the HTML portion in a browser tab automatically.

This is done by adding this to your ~/.mailcap:

  text/html;  mutt_bgrun /usr/bin/firefox %s >/dev/null 2>&1; needsterminal
  text/html; elinks -dump ; copiousoutput

(where `mutt_bgrun` is here: https://www.mattcutts.com/files/mutt_bgrun)

And then on ~/.muttrc:

  macro index,pager ,b "<view-attachments>/html<enter><view-mailcap><exit>" "View first HTML attachment in browser"

That way, if I'm on an e-mail and I want the actual HTML rendering, I hit ",b" and it goes to a browser tab.