I’d try changing the order of your rules. Once the default WP rules run, your URL will be rewritten and your last rule won’t work.
SetEnv no-gzip dont-vary
RewriteEngine On
RewriteRule ^produse/piese-schimb-utilaje-agricole/([0-9]+)/?$ ^produse/piese-schimb-utilaje-agricole/?listpage=$1&search_field=none&value=&operator=LIKE&sortBy=denumire&ascdesc=asc&submit=&sortstring=denumire&orderstring=asc#participants-list [NC,L]
# Turn mod_rewrite on
RewriteEngine On
RewriteBase /
RewriteRule ^index\.php$ - [L]
# add a trailing slash to /wp-admin
RewriteRule ^([_0-9a-zA-Z-]+/)?wp-admin$ $1wp-admin/ [R=301,L]
RewriteCond %{REQUEST_FILENAME} -f [OR]
RewriteCond %{REQUEST_FILENAME} -d
RewriteRule ^ - [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(wp-(content|admin|includes).*) $2 [L]
RewriteRule ^([_0-9a-zA-Z-]+/)?(.*\.php)$ $2 [L]
RewriteRule . index.php [L]