Should Hindus study Hinduism? Or, for that matter, anything that is not prima facie germane to their vocational aspirations? There are two good reasons why they definitely should study Hinduism: one from the perspective of the philosophy of religions, and one from the perspective of Hindu "theology," specifically from the perspective of Mādhva Vedānta.
Most students who enroll in my classes are unaware of the foundations of the beliefs that they have, or for that matter, that they have any beliefs at all. If a student, Hindu or otherwise, is inspired to become aware of, and question, her/his own presuppositions (be these ontological, epistemological, soteriological or otherwise), and perhaps even to entertain the possible truth of those put forth by others, then the class, and their college education has served one of its most important purposes, namely to think critically, and in this case, to think critically about perhaps fundamental beliefs. By studying Hinduism, Hindu students may have their belief confirmed and challenged. These confirmations and challenges may be internal, after thoughtful self-reflection, or may come from external sources, from peers who are also suddenly discovering their beliefs and having them confirmed and challenged.
So should students become aware of their own beliefs, learn to think about them using historical, anthropological, sociological, psychological, political tools? Should Hindus study Hinduism? Should they become enlightened about their core philosophical presuppositions?
Of course they should.
The philosophical and religious schools of Hinduism all shared a belief in the mechanism of karma, that one's actions in earlier lives affected both one's rebirth and the events that are to occur in one's future lives. The entity that was reborn is the ātman (enduring self). One accumulates some combination of puṇya (meritorious karma) and pāpa (demeritorious karma) -- popularly rendered in the West as "good" and "bad" karma -- and is born again and again in saṃsāra (worldly existence). The philosophical and religious schools of Hinduism also all shared an interest in ending this seemingly endless cycle, and this desire was their raison d'être. The state that sentient beings enter after being liberated from the cycle is called mokṣa.
Each school of thought offered methods by which adherents could break the cycle and attain the desired end. Many (but not all) of the schools of Hinduism required that adherents become virtuoso readers of texts held to be salvifically efficacious, texts that would teach virtuosos about the right (and wrong) cognitive habits and practices that led to mokṣa (or led to rebirth).
The Mādhva school of Vedānta, founded by Madhvācārya (1238-1317 C.E.) in the 13th century in the Karnataka state of India, puts forth a strong position that mokṣa is only possible after becoming a virtuoso reader. Insofar as Mādhva Vedānta is a Hindu tradition, it thus puts forth the position that, unequivocally, Hindus should study Hinduism.
Mādhva Vedānta, is, not surprisingly, a school of Vedānta. Vedānta was and is a commentarial tradition that holds the Vedas, specifically the Upaniṣads, to be its root texts. The Upaniṣads were thus central to Vedānta commentary. The Brahma Sūtras (also called the Vedānta Sūtras), composed by Bādarāyaṇa (also known as Vyāsa) in the fifth century C.E., is regarded as a systematization of the teachings of the Upaniṣads. Above all, the Brahma Sūtras characterized the nature of the relationship between Brahman (the divine principle) and the ātman (individual self). Knowledge of this relationship would lead to mokṣa (liberation) from saṃsāra (the cycle of birth and rebirth).
The injunction to become a virtuoso reader is explicit in the first sūtra (decree) of Brahma Sūtras of Bādarāyaṇa: athāto brahmajijñāsā. Madhvācārya explains this in his Bhāṣya (commentary) on the Brahma Sūtras of Bādarāyaṇa. The expanded passage that takes Madhvācārya's commentaries into account is: "Therefore, after having met the requirements for eligibility, the inquiry into brahman is to be undertaken." If one claims to be a Hindu and upholds the centrality of the Brahma Sūtras and the Upaniṣads, both deemed Hindu texts, then it is essential for one to study and to become virtuoso.
Madhvācārya further explains that: "In the Nārada Purāṇa it is stated: "Hearing [the text], reflecting [on the text], also meditating, and also being devoted are the important means of securing knowledge [of the lord]. No other is shown [to be a means of securing such knowledge]. And without these [activities], no one obtains knowledge from anywhere else."  Study may result in enlightenment.
For some schools of Hinduism it is essential for Hindus to study Hinduism.
Hindus should indeed study Hinduism. Such critical self-reflection is part of a college education. It also behooves Hindus to know something about the history of "Hinduism." It essential to make the familiar unfamiliar and to learn something about ones beliefs, to learn what one presupposes. And from the perspective of Mādhva Vedānta, studying Hinduism and eventually becoming a virtuoso reader of Hindu texts, is a prerequisite for mokṣa.
Hindu students should study Hinduism.
Enlightenment (and a college degree) may follow!
 athaṡabdo maṇgalārtho 'dhikārānantaryārthaṡ ca | ataḥsabdo hetvarthaḥ | Madhvācārya Brahma Sūtra Bhāṣya, 1.1.1
"The word 'then' is used [both] as an auspicious expression and [in reference to] the sequence of eligibility. The word 'therefore' refers to the reason."
 ṡravaṇaṃ mananaṃ caiva dhyānaṃ bhaktis tathaiva ca | sādhanaṃ jñānasampattau pradhānaṃ nānyadiṣyate || na caitāni vinā kaṡ cijjñānamāpa kutaṡcane 'ti nāradīye | Madhvācārya Brahma Sūtra Bhāṣya, 1.1.1.