Yes, the reform and conservative movements have a ridiculous custom,
where on Parshas Noach, the congregants are invited to bring in their pets for a special Birchas Kohanim service. Followed by kaddish for their deceased companions.
The custom comes from the Catholic and Episcopalian churches, who celebrate the teachings of St. Francis of Assisi, the patron saint of animals, by blessing animals on October 4th.