The Waldensians were followers of Peter Waldo. I don’t know much about him or the sect, but I can look into it.
The Albigensians were not peaceful people in general.
They believed in two equal gods, one good who created
spirit (invisible) things, and one bad who created the material world (the universe, the planets, animals, our bodies, etc. the whole material shebang). Because of these weird beliefs, they believed that marriage was intrinsically evil and sinful, all the more so because the joining of two material bodies was blessed in the name of God, which they considered blasphemous. Fornication was to be preferred over marriage because at least the good god wasn’t asked to bless the fornication. Suicide was considered a very highly virtuous act because the person committing suicide was setting his pure and holy soul FREE from the inherently wicked and sinful body (not sinful because of the Fall, but sinful because it was material). Hence, Albigensianism was grossly immoral and extremely activist. It was a very real danger not only to the peace and wellbeing of the Church and the Faithful, but also a very real threat to the established moral order of the State, which based it’s laws on Christian moral teaching.
Yes, the Church responded by asking the State to attack the Albigensians, but the Albigensians started it. Also, many who had fallen for the lies of Albigensianism were reconverted to the Catholic Faith by the preaching of holy priests.