Adding the mini-cart element in Cornerstone has the following classes for the “view cart” and “checkout” buttons:
<a href="#" class="button wc-forward wp-element-button">View cart</a>
<a href="#" class="button checkout wc-forward wp-element-button">Checkout</a>
This allows for the styling in Cornerstone settings to style it. But on the front end they are missing the class
button so they render differently from the preview.
On the frontend the classes are as follows:
<a href="#" class="wc-forward wp-element-button x-anchor">
<a href="#" class="checkout wc-forward wp-element-button x-anchor">
Also in Cornerstone the mini-cart element ‘buttons’ tab doesn’t have an option for the background colors, but you can change the text colors. However, any changes here does not affect the preview, only the front end.