This patch is taken from Debian, using Debian version 1.7.0-8.
A new patch will be needed when apr is updated.

# quick and dirty fix for FTBFS on mipsel
# There should be a proper configure check, see 
# https://bz.apache.org/bugzilla/show_bug.cgi?id=63566
Index: apr-1.7.0/include/arch/unix/apr_arch_atomic.h
===================================================================
--- apr-1.7.0.orig/include/arch/unix/apr_arch_atomic.h
+++ apr-1.7.0/include/arch/unix/apr_arch_atomic.h
@@ -26,6 +26,9 @@
 /* noop */
 #elif HAVE_ATOMIC_BUILTINS
 #   define USE_ATOMICS_BUILTINS
+#   if (__INTPTR_WIDTH__ == 32) && ( defined(__MIPSEL__) || defined(__powerpc__) ) || defined(__m68k__) || defined(__sh__)
+#       define NEED_ATOMICS_GENERIC64
+#   endif
 #elif defined(SOLARIS2) && SOLARIS2 >= 10
 #   define USE_ATOMICS_SOLARIS
 #   define NEED_ATOMICS_GENERIC64
Index: apr-1.7.0/atomic/unix/builtins64.c
===================================================================
--- apr-1.7.0.orig/atomic/unix/builtins64.c
+++ apr-1.7.0/atomic/unix/builtins64.c
@@ -16,7 +16,7 @@
 
 #include "apr_arch_atomic.h"
 
-#ifdef USE_ATOMICS_BUILTINS
+#if defined(USE_ATOMICS_BUILTINS) && ! defined(NEED_ATOMICS_GENERIC64)
 
 APR_DECLARE(apr_uint64_t) apr_atomic_read64(volatile apr_uint64_t *mem)
 {
Index: apr-1.7.0/atomic/unix/builtins.c
===================================================================
--- apr-1.7.0.orig/atomic/unix/builtins.c
+++ apr-1.7.0/atomic/unix/builtins.c
@@ -20,7 +20,11 @@
 
 APR_DECLARE(apr_status_t) apr_atomic_init(apr_pool_t *p)
 {
+#if defined (NEED_ATOMICS_GENERIC64)
+    return apr__atomic_generic64_init(p);
+#else
     return APR_SUCCESS;
+#endif
 }
 
 APR_DECLARE(apr_uint32_t) apr_atomic_read32(volatile apr_uint32_t *mem)
ck.tmpl'>
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<div class='path'>path: <a href='/guix/log/?id=166f943b53a9f4bb35a79de4243a62e61dda9131'>root</a>/<a href='/guix/log/gnu?id=166f943b53a9f4bb35a79de4243a62e61dda9131'>gnu</a>/<a href='/guix/log/gnu/system?id=166f943b53a9f4bb35a79de4243a62e61dda9131'>system</a>/<a href='/guix/log/gnu/system/examples?id=166f943b53a9f4bb35a79de4243a62e61dda9131'>examples</a>/<a href='/guix/log/gnu/system/examples/beaglebone-black.tmpl?id=166f943b53a9f4bb35a79de4243a62e61dda9131'>beaglebone-black.tmpl</a></div><div class='content'><table class='list nowrap'><tr class='nohover'><th class='left'>Age</th><th class='left'>Commit message (<a href='/guix/log/gnu/system/examples/beaglebone-black.tmpl?id=166f943b53a9f4bb35a79de4243a62e61dda9131&amp;showmsg=1'>Expand</a>)</th><th class='left'>Author</th></tr>
<tr><td><span title='2023-03-03 17:55:32 +0100'>2023-03-03</span></td><td><a href='/guix/commit/gnu/system/examples/beaglebone-black.tmpl?id=4892c0186eec75253701c5097803b6168a2956ce'>services: base: Deprecate 'agetty-service' procedure.</a><span class='msg-avail'>...<span class='msg-tooltip'>* doc/guix.texi (Base Services): Replace agetty-service with
agetty-service-type.
* gnu/services/base.scm (agetty-service): Deprecate procedure.
* gnu/system/examples/beaglebone-black.tmpl
(operating-system)[services]: Use agetty-service-type.

Signed-off-by: Ludovic Courtès &lt;ludo@gnu.org&gt;
</span></span></td><td>Bruno Victal</td></tr>
<tr><td><span title='2022-12-16 23:42:17 -0500'>2022-12-16</span></td><td><a href='/guix/commit/gnu/system/examples/beaglebone-black.tmpl?id=491bddfa276cc9775adf325c07e5f82638f330e7'>system: examples: Add mode prop line.</a><span class='msg-avail'>...<span class='msg-tooltip'>* gnu/system/examples/asus-c201.tmpl: Add a mode prop line.
* gnu/system/examples/bare-bones.tmpl: Likewise.
* gnu/system/examples/beaglebone-black.tmpl: Likewise.
* gnu/system/examples/desktop.tmpl: Likewise.
* gnu/system/examples/docker-image.tmpl: Likewise.
* gnu/system/examples/lightweight-desktop.tmpl: Likewise.
* gnu/system/examples/raspberry-pi-64-nfs-root.tmpl: Likewise.
* gnu/system/examples/raspberry-pi-64.tmpl: Likewise.
* gnu/system/examples/vm-image.tmpl: Likewise.
</span></span></td><td>Maxim Cournoyer</td></tr>