Does the Hadith, "If someone whose religiosity and character you approve comes to you, then marry him. If you do not do so, there will be tribulation on earth and widespread corruption," mean that it is impermissible to marry someone whose character is not approved of, such as a liar, for example?

The hadith encourages choosing a person of good religious commitment and character, but this is understood as a recommendation, not an obligation. If a person is not pleasing in their religious commitment and character, like a liar, then they are not a suitable match for a righteous Muslim woman, and she should not be married to him. Lying leads to immorality, and immorality leads to the Hellfire. However, if the marriage contract is concluded with a husband who is immoral and not a suitable match, the marriage is valid according to most scholars. Compatibility is not a condition for marriage according to the majority of them. The woman and her guardian may forgo compatibility in religious commitment and accept an immoral person, and the marriage is valid according to the well-known opinion if she feels safe from the immoral person.