Basic Auth .htaccess on wp-login, but allow logout from woocommerce

From the answer in Password protect a specific URL, we can reverse the condition. To quote his answer,

You should be able to do this using the combination of mod_env and the
Satisfy any directive. You can use SetEnvIf to check against the
Request_URI, even if it’s not a physical path. You can then check if
the variable is set in an Allow statement. So either you need to log
in with password, or the Allow lets you in without password:

# Do the regex check against the URI here, if match, set the "require_auth" var
SetEnvIf Request_URI ^/shop/my-account/customer-logout/ require_auth=false

# Auth stuff
AuthUserFile /var/www/htpasswd
AuthName "Password Protected"
AuthType Basic

# Setup a deny/allow
Order Deny,Allow
# Deny from everyone
Deny from all
# except if either of these are satisfied
Satisfy any
# 1. a valid authenticated user
Require valid-user
# or 2. the "require_auth" var is NOT set
Allow from env=!require_auth