Quickly summarized--

Some of the following issues can be described as insensible.

Unfortunately in today's times some people are willing to renounce their family and their family name because of the little they heard about a chapter in American history called slavery.

The Thornton name goes back long before slaves were traded and shipped, referring to the 1400 to the 1800s in the USA.

Some descendants of Thornton of European stock married with other ethnicities, such as American Indian, possibly African American, included and not limited to.  That they do not 'belong' nor have the rights to claim Thornton as ancestors in the same sense as those with European stock today, is not really a matter on the mark of matters that have true weight.  Everything is commensurate to what it really is.

The Thornton name goes back long before immigrants came to America, married with other tribes in the USA, referring to post 1400

Renouncing Thornton name, or even in effect ancestry, due to religion.

The Thornton name goes back long before Anglicization in England and America, that took place post the one some call Peter, sometimes referred to as the first Pope era.  Some may choose to retain the name on legal records, some may choose not to, or to 'change' their name.  What is right and what is wrong, correct and incorrect, in some instances, let their Lord be the judge.

Civil War.  According to some military records hundreds of soldiers with surname Thornton fought on the Confederacy.  While only a few with Thornton surname fought on the side of the Union. Along comes the discussion of family ties due to the splits in War.

The Thornton name goes back long before the Civil War.