I think that you need to use math-mode to some extent, however, you can reduce the number of \text{...} statements that you need if you use the rcases* environment from the mathtools package:
\[
\begin{rcases*}
& inclusive\\
& opposite\\
& casual \\
& parallel\\
\end{rcases*}\text{relationship}
\]
This produces:

If you want to pretend that you are not using math-mode then you could wrap this into a command. The easiest way to do this is to define a command, say \MyCases, that takes a comma separated list of the cases that appear to the left of the brace together with the text that appears on the right. With this in place, you would be able to produce the output above using
\MyCases{inclusive, opposite, casual, parallel}{relationship}
The output is essentially the same as before. Here is the full code:
\documentclass{article}
\usepackage{mathtools,etoolbox}
% \MyCases{comma separated list of cases}{right hand text}
\newcommand\MyCases[2]{%
\[
\renewcommand*{\do}[1]{&##1\\}% a line in the rcases* environment
\begin{rcases*}
\docsvlist{#1}% add the cases
\end{rcases*}\text{#2}
\]
}
\begin{document}
\[
\begin{rcases*}
& inclusive\\
& opposite\\
& casual \\
& parallel\\
\end{rcases*}\text{relationship}
\]
\MyCases{inclusive, opposite, casual, parallel}{relationship}
\end{document}
A few remarks about how the \MyCases command works. The key point is to use the \docsvlist command from the etoolbox package to loop over the contents of the comma separated list. This is done by redefining the \do command. After this, we are essentially just doing what I did above using the rcases* environment.
\texteverywhere that you want it "outside math mode"? – Werner Apr 08 '20 at 02:09