Which has a greater claim to judgment: the religion of Allah or the religion of people, taking into consideration that the right of Allah is based on forgiveness, while the rights of people are based on strictness?

The issue you are asking about cannot be addressed by simply stating that the rights of people take precedence over the rights of Allah or vice-versa; rather, it involves detailed explanations. Examples where the rights of people are given precedence over the rights of Allah, out of leniency towards them, include: uttering a word of disbelief under duress, excuses that permit missing congregational prayers, Friday prayers, and Jihad, and delaying fasting due to illness or travel. As for issues where there is a difference of opinion regarding whether the rights of Allah or the rights of people take precedence, these include: giving precedence to zakat over debts when a person dies. The preferred view is to give precedence to zakat, based on the Prophet's (peace be upon him) saying: "The debt owed to Allah is more deserving of being fulfilled," and because zakat involves a right for Allah and a right for the poor. Another example is the convergence of Hajj and debts for the deceased, concerning which there are several opinions, including giving precedence to Hajj due to the textual evidence, or giving precedence to the debt, or treating them equally if someone is found to perform Hajj on a pro-rata basis.