One could say that their faith was just a residual of their early education, one they did not manage to get rid of, but this is not the case, since at least some of them (e.g. Veṅkaṭanātha), wrote also mature theological treatises. Or, one could suppose that god was for them just a useful part of their philosophical systems (as he happened to be at a certain point of the history of Vaiśeṣika –according ot J. Bronkhorst's interpretation– where he played the role of warranty of karman), but this is also not the case, since the Mīmāṃsā school is explicitly based on the rejection of whatever is not a) empirically ascerteined, b) absolutely needed and at the same time a priori non graspable by the instruments of knowledge. Now, a god as part of the system is not empirically ascertained, nor is ne absolutely needed. The system works smoothly, as we all see, as it is. Thus, the introduction of a god is not for the sake of the system as it is, but rather for the sake of justifying a previous or later stage of the system. And there is no need to imagine that the system has ever had any previous or later stages.
What is left out, instead, is the case of something which is not graspable by our senses (lato sensu) and still is not just superstition. Is there anything like that?
Mīmāṃsakas are sure that such a sphere exists, insofar as our senses do not grasp anything but what exists. They have no jurisdiction over what should be. No matter how long one observes someone stealing cars, one will never realise that this is wrong just through sense-perception. Instead (so the Mīmāṃsā argument), one will need an authority explaining that this ought to be punished.
Now, some scientists have tried to argue that moral thinking can be explained through scientific laws, and, thus, that there is no separate realm of what ought to be. Our moral thought is just the result of, e.g., evolution, and it could not be different. It belongs to the realm of the is (rather than to the realm of the ought). Do you find these explanations convincing? Why or why not?
On Veṅkaṭanātha, see this post. On theism and atheism in India, see this post.