Is it possible to Take Refuge in the Three Jewels, but still learn spiritual wisdom from teachers in other religions?

The short answer is Yes, you can still take refuge to the three Jewels and follow a spiritual path that does not Contradict nor Deny the three Jewels.

If I were you, I would only be concerned if the other religions will prolong/delay your path in reaching enlightenment, even if it is possible.

Is it possible to Take Refuge in the Three Jewels, but still learn spiritual wisdom from teachers in other religions?

It depends on the content of those other religious teachings. If they contain aspects such as a Creator God, a permanent Soul etc. it would pose quite a problem for the advancement on the Buddhist path.

The Buddha's teaching is first and foremost a practical teaching emphasizing an experiental understanding of reality, rather than an intellectual understanding. There is not a belief-system in place as seen in e.g. Islam and Christianity.

The Buddha's teaching is described as "Ehi-passiko", directly translated it means something close to "come-and-see" or "one-is-invited-to-come-and-see-for-oneself". The teaching is "come-and-seeable". It means that the practitioner of the Buddhist path becomes his or her own refuge, not relying on blind belief but instead through correct and consistent practice develops a correct understanding (Right View: Sammā-diṭṭhi) of reality.

The Buddha's teaching is designed to expel Ignorance (Avidyā), which is one of the basic causes for beings to take rebirth. The insight-portion of the teaching is designed to make the meditator gain access to the Signs of Existence, i.e. the impermanent, unsatisfactory and uncontrollable nature of conditioned reality. Impermanence is masked by the illusion of continuity, which again masks the unsatisfactory nature of phenomena. Ignorance is what keeps this illusion going.

Vipassana meditation expels ignorance which in turn allows practitioners see reality clearly. When one truly sees that nothing in the world is worth clinging to and that conditioned phenomena is unreliable, oppresive and cause constant suffering due to their incessant arising and ceasing, the mind simply gives it up and becomes free.

If one is mixing the Buddhist teaching with other religious teachings that are based on blind belief or concepts such as a Creator God, a Soul etc., one is adding more ignorance to ones one mind stream, meaning one creates further distance between oneself and liberation. Following other religious teachings might be possible but it might also make ones own progress towards Nibbana slower or even impossible.

When it is said that one's refuge "is broken whenever a person goes for refuge to a teacher outside the Buddha's Dispensation[...]" the meaning is that one should not go for ultimate refuge in anything but the three Jewels. It is Lama Je Tsongkhapa's interpretation.

When one is sick, (1) fearing the suffering of illness and (2) trusting that the doctor can protect him from it, he goes to the doctor to seek protection. This is called taking refuge. But this is not ultimate refuge.

A Buddhist can uphold this type of refuge. Other common instances are: relying on a deity or a spirit in the hope of being prosperous... or having children... or having good crops, etc. These are worldly concerns.

Now, the Buddha is the one true doctor that can protect you from the suffering of cyclic existence, as well as from the suffering caused by self-cherishing (that impedes you from being able to benefit other sentient beings). There are these two "definite goodness": (1) individual liberation, and (2) complete buddhahood.

One cannot go for refuge to anything but the three Jewels to obtain either of these two definite goodnesses, thereby becoming a holly being, a saint, a foe destroyer an arhat. The actual foes (afflictive obscurations and knowledge obscurations) cannot be destroyed but by actualizing the three Jewels in one's continuum.

There is no issue for you to attend Muslims or Christian, etc. teachings and drawing conventional wisdom from them at all. The most important is that it helps you destroy the foes, the enemies of ignorance and self-cherishing. A Theravada might say: as long as it helps you destroy the foe of craving, but you get the gist.

This morning still, I sent a passage from Rudolph Otto (a Lutheran theologian) to a brother of mine, also a Buddhist monk. The quote went:

For one of the chiefest and most general features of mysticism is just this self-depreciation (so plainly parallel to the case of Abraham), the estimation of the self, of the personal "I," as something not perfectly or essentially real, or even as mere nullity, a self-depreciation which comes to demand its own fulfillment in practice in rejecting the delusion of selfhood, and so makes for the annihilation of the self. And on the other hand mysticism leads to a valuation of the transcendent object of its reference as that which through plenitude of being stands supreme and absolute, so that the finite self contrasted with it becomes conscious even in its nullity that "I am naught, Thou art all."

And that can definitely speak to Buddhist yogis.