How can my theme allow users to take advantage of advanced html tags in posts

About the link you provided

The black bar is part of the .pagewrapper but there is no width specified for pagewrapper.

.pagewrapper {
  left: 0;
  position: relative;
  transition: left 500ms ease-in-out 0s;
}

The post content is set a max-width: 700px, it will not extend the boundary.

.wrapper {
  margin: 0 auto;
  max-width: 700px;
  width: 90%;
}

The black bar is entirely new section which has this code, no width set for it:

.postcontents.dark {
  background: none repeat scroll 0 0 #2c2e32;
  color: #e2e2e2 !important;
  padding: 90px 0;
}

There is a CSS specific solution.

If you need to use the block quote which is 100% of the width, you need to make it come out of the normal flow of the #container.

.blockquote {
  position: absolute;
  width: 100%;
  left: 0;
}

Blockquote within container
Blockquote within container

Blockquote outside the flow
Blockquote outside the flow

A better solution will be to create a custom class called blockquote-full-width and allow the users to use it.