How can I change the line distances without affecting the footnote distances?

For those using Memoir class: \setstretch{1.25} will give an error; no (big) problem!
Just add the line \DisemulatePackage{setspace} before \usepackage{setspace}:

\DisemulatePackage{setspace}
\usepackage{setspace}
\setstretch{1.25}

The above worked for me.
(Thanks to another contributor for this hint with Memoir class.)

do not change the value of \baselinestretch. Use package setspace instead:

\documentclass{article}                 
\usepackage[english]{babel} 
\usepackage{setspace} 
\usepackage{blindtext} 
\setstretch{1.25}
\begin{document}            

\blindtext\footnote{\blindtext}

\end{document}