"Peace and tolerance" are underpinned by their belief that muslims should unite against their common enemy which they believe is Western dominance of Islamic Ummah, in particular US and Israeli domination/occupation. This resonates with the call by the late founder of Islamic Republic of Iran, Ayatollah Khomeini for Islamic unity and resistance against the West, and that's also one reason the Houthis are claimed to be supported or influenced by Iran. The other ground for their tolerance is their opposition to Salafism/Al-Qaeda which is widely known as an intolerant, extremist and terrorist Islamic group which has engaged in sectarian infighting and division in the Islamic Ummah rather than staging any real, honorable resistance against Western domination. They have in fact destroyed the public image of Islam by committing all sorts of wrongs and excesses such as indiscriminate violence against non-Salafists and non-mulims and pretty much anyone who doesn't adopt their ideology. I'm elaborating on this to help better make sense of the Houthi ideology and such characterizations offered by the Yemeni professor. Also see how this is in line with the Newsweek identification of Houthi descent cause as being shared by all Yemenis. Houthis are genuinely inspired by Shia Islam but that's also exactly why they are striving for indiscriminate well-being of all muslims. You need to study about Shia Islam to understand this, especially Shia distinct appreciation for reason and universal justice.