The underscores and carrots are highlighted red which is really an eyesore. How can I change/remove this?
The plugin works fine, so I don't think it's an installation issue.
Update for more details:
Vim 8.1, I doubt I have any conflicting plugins. I have a tex.vim file located at /usr/local/share/vim/vim81/syntax/.

vimversion are you using and do you have any other plugins that could come into conflict with the LaTeX plugin? – Nov 25 '19 at 23:37