What is the ruling on fulfilling a vow to go out with the Tablighi Jamaat after marrying so-and-so, knowing that there are statements from senior scholars considering going out with them an innovation?

There is no contradiction between the website's fatwa and the fatwa of senior scholars regarding the ruling on Jama'at al-Tabligh. The website qualified its fatwa by the existence of a group that adheres to the Sunnah, which aligns with what the website quoted from Sheikh Ibn Baz - may Allah have mercy on him - that the ruling on groups is tied to their actual situation: what among them conforms to the truth is accepted, and what contradicts it is rejected, and this is determined by the people of knowledge. The website also quoted Sheikh Ibn Uthaymeen - may Allah have mercy on him - affirming his support for the group in the Kingdom based on his awareness of their methodology there. The website holds that the ruling on groups is based on their scholarly and practical methodology and their books, not merely on the name.