I guess facts are only strings, not booleans. Or I need to learn more.

facts/system.yml

@@ -3,7 +3,7 @@
 
 - name: Set Pop OS Facts
   set_fact:
-    flatpak_distro: yes
+    flatpak_distro: true
     lynis_install_dir: /usr/local/lynis
     lynis_report: /home/ling/lynis.log
     sudoers_install_dir: /etc/sudoers.d/ansible
@@ -13,7 +13,7 @@
 
 - name: Set Debian and Ubuntu Facts
   set_fact:
-    flatpak_distro: yes
+    flatpak_distro: true
     lynis_install_dir: /usr/local/lynis
     lynis_report: /root/lynis.log
     sudoers_install_dir: /etc/sudoers.d/ansible
@@ -23,7 +23,7 @@
 
 - name: Set FreeBSD Facts
   set_fact:
-    flatpak_distro: no
+    flatpak_distro: false
     lynis_install_dir: /usr/local/lynis
     lynis_report: /root/lynis.log
     sudoers_install_dir: /usr/local/etc/sudoers.d/ansible

local.yml

@@ -32,10 +32,10 @@
   tasks:
     - include: tasks/linux/flatpaks.yml
       when: ansible_system == "Linux" and
-            flatpak_distro == yes
+            flatpak_distro == "true"
     - shell: echo "Not implemented yet. :("
       when: ansible_system == "Linux" and
-            flatpak_distro == no
+            flatpak_distro != "true"
     - include: tasks/freebsd/gui.yml
       when: ansible_system == "FreeBSD"