LGBTQ by itself is not a threat to either Putin or Xi but what LGBTQ represents is a threat to traditional society and gender roles. The judgement is still out if new type of society developed in the west with modern gender norms, women’s rights and sexual freedoms is viable long term and from demographic perspective it’s frankly probably not.
Authoritarians instinctively cling to the old roles/family and even if are not able to fully stop changes (US is amazing at exporting ideology) they try to and battle against LGBT is part of that fight.
I do not think you can directly connect authoritarian and being anti LGBQ outside of modern context - Xi, Putin or Orban views on lgbt were mainstream in US only 20-30 years ago.
Authoritarians instinctively cling to the old roles/family and even if are not able to fully stop changes (US is amazing at exporting ideology) they try to and battle against LGBT is part of that fight.
I do not think you can directly connect authoritarian and being anti LGBQ outside of modern context - Xi, Putin or Orban views on lgbt were mainstream in US only 20-30 years ago.