Chinese Buddhists consider all people to be potential Buddhas

Yes. But all schools of Buddhism say it is possible for any being to become a Buddha, but given their rarity unlikely - and a Buddha is specifically an originator of the teaching in a realm without one, so as long as Buddhism exists, there can't be a new Buddha only arhats and bodhisattvas. There is a long tradition not only in Chinese Buddhism, of recognising the wisest teachers of other traditions as pratyekabuddha, those who have some degree of awakening but do not teach it's full realisation. Lao Tzu has been widely identified as such a one.

Scholars have linked the emphasis on the tathatagharba doctrine of original enlightenment or Buddha-nature in Chinese Buddhist schools, to it's resonance with the Dao and principle of Li in Confucianism, which are doctrines of natural or original harmony.

The doctrine draws from Buddhas description of the 'luminous mind':

"Luminous, monks, is the mind. And it is defiled by incoming defilements" -Anguttara Nikaya, 1.49-52 (alternative translations and Therevada discussion of here)

And

"He whose faith in the Tathagata is settled, rooted, established, solid, unshakeable by any ascetic or Brahmin, any deva or mara or Brahma or anyone in the world, can truly say: 'I am a true son of Blessed Lord (Bhagavan), born of his mouth, born of Dhamma, created by Dhamma, an heir of Dhamma.' Why is that? Because, Vasettha, this designates the Tathagata: 'The Body of Dhamma,' that is, 'The Body of Brahma,' or 'Become Dhamma,' that is, 'Become Brahma.'"" -Digha Nikaya III. 84

The tenth chapter of The Lotus Sutra, emphasises that everyone can be liberated, that all living beings can become a buddha, not only monks and nuns, but also laypeople, and non-human creatures. It also details that all living beings can be a 'teacher of the Dharma'. The Lotus Sutra is foundational for and of the highest prominence in Tiantai, Tendai, Cheontae, and Nichiren schools. But also important in Chinese Zen, and there is a commentary on it by Vasubhandu in the Therevada tradition. A copy of The Lotus Sutra is the world's oldest printed book, bound in blue silk, and is held in the British Library in London. Worth dropping in to see if you're there.

It is interesting to note the dharmakaya within the trikaya doctrine in Chinese thought. The trikaya are the three bodies of a Buddha, the nirmankaya or 'transformation-body' is a physical manifestation of a Buddha in the world. The sambhogakaya or 'bliss-body' is the celestial manifestation. And the dharmakaya or 'dharma-body' is the unmanifested "inconceivable" (acintya) aspect of a Buddha out of which Buddhas arise and to which they return after their dissolution. It's interesting to me, to notice parallels with Christian theology, both of the trinity, and specifically of immanence. The framing I choose, is to see religious practice and doctrinal innovation as about succeeding in helping practicioners and communities of practicioners to succeed, and live well. So I note this as a kind of convergent-evolution that highlights the doctrines effectiveness.

Do they believe that only the minds of Buddhists can come to enlightenment?

In the Maha-Parinibbana Sutta: The Great Discourse on the Total Unbinding, the Buddha teaches that "in any doctrine or discipline" that does not contain the Noble Eightfold Path, enlightened beings cannot be found:

Then Subhadda went to the Blessed One and exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there, he said to the Blessed One, "Venerable sir, these brahmans & contemplatives, each with his group, each with his community, each the teacher of his group, an honored leader, well-regarded by people at large — i.e., Purana Kassapa, Makkhali Gosala, Ajita Kesakambalin, Pakudha Kaccayana, Sañjaya Belatthaputta, & the Nigantha Nataputta: Do they all have direct knowledge as they themselves claim, or do they all not have direct knowledge, or do some of them have direct knowledge and some of them not?"

"Enough, Subhadda. Put this question aside. I will teach you the Dhamma. Listen, and pay close attention. I will speak."

"Yes, lord," Subhadda answered, and the Blessed One said, "In any doctrine & discipline where the noble eightfold path is not found, no contemplative of the first... second... third... fourth order [stream-winner, once-returner, non-returner, or arahant] is found. But in any doctrine & discipline where the noble eightfold path is found, contemplatives of the first... second... third... fourth order are found. The noble eightfold path is found in this doctrine & discipline, and right here there are contemplatives of the first... second... third... fourth order. Other teachings are empty of knowledgeable contemplatives. And if the monks dwell rightly, this world will not be empty of arahants."

Buddhism holds that any being can become enlightened if they follow the Buddha's teachings. Different sects of Buddhism envision it on different timescales, and different sects have different relationships to the ideal, but no Buddhist would ever say: "This person (or these people) can never achieve enlightenment".

It's a more open question whether one must identify as a Buddhist to achieve enlightenment. As I see it, someone of a different faith (a Christian, Muslim, Hindu, Jew, Jain, Atheist, or what you will) who follows the teachings of the Buddha as well as their own beliefs should have no problem attaining; someone who follows no path at all, but uses practices that are (for all practical purposes) the same as what the Buddha taught should have no problem attaining. Enlightenment is a realization, not a thing or event. The Buddha showed a path and practices that lead us in the direction of that realization, but ultimately even the identification of 'being a Buddhist' must fall by the wayside.