Glossaries package: small caps in body and normal caps in the acronym list

Change the meaning of \acronymfont when you want to typeset the list (but I don't think it's a good idea).

\documentclass[a4paper]{report}
\usepackage[style=long, toc, smallcaps]{glossaries}
\makeglossaries
\newacronym{acr}{acr}{Acronym}

\begin{document}

This is an \gls{acr}. An \gls{acr} should be in small caps.
The first column in the following list of acronyms should be in normal caps.

\begingroup
\let\clearpage\relax % this line is just not to have a page break
\renewcommand{\acronymfont}[1]{\MakeUppercase{#1}}
\printglossary[title={List of Acronyms}]
\endgroup

\end{document}

Page 123 of the glossaries' user manual reads:

\glossaryentryfield{<label>}{<formatted name>}{<desc>}{<symbol>}{<number list>}

This macro indicates what to do for a given glossary entry. Note that <formatted name> will always be in the form \glsnamefont{<name>}. This allows the user to set a given font for the entry name, regardless of the glossary style used.

With this in mind, one solution to your problem is to change the definition of \glsnamefont:

\documentclass[a4paper]{report}
\usepackage[style=long,smallcaps]{glossaries}

\newacronym{acr}{acr}{Acronym}

\renewcommand{\glsnamefont}[1]{\MakeUppercase{#1}}

\immediate\write18{makeglossaries \jobname} % run (pdf)latex twice with --shell-escape
\makeglossaries

\begin{document}
\gls{acr}; \gls{acr}.
\printglossary[title={List of Acronyms}]
\end{document}