Is the inquirer's marriage to her husband invalid, knowing that he believes in God and the Prophet, may God's prayers and peace be upon him, but he holds the view that the teachings of Islam are not necessarily for application at the present time?

The Prophet, peace and blessings be upon him, recommended marrying a person of faith, because marriage to an atheist is invalid, and the contract is Islamically annulled. It is not permissible for a woman who believes in Allah and the Last Day to proceed with such a corrupt marriage under the pretext that the man might change after marriage. As Allah Almighty says: (O you who have believed, when the believing women come to you as emigrants, then test them. Allah is most knowing of their faith. And if you ascertain that they are believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them. And give them what they [disbelievers] have spent. And there is no blame upon you if you marry them when you have given them their due compensation. And do not hold on to the marriage bonds of disbelieving women). The husband's statement that "what matters is a pure heart, and it doesn't matter if one drinks alcohol or gambles" is false. Islam is a message for all people until the Day of Judgment, and the effect of a righteous heart must be manifested in one's limbs. In summary: your marriage is corrupt and invalid, and it is not permissible for you to allow him access to yourself until he returns to Islam and adheres to the rulings of Sharia. If he does not do so, the contract must be annulled Islamically, or you should seek a divorce or khul'.