The difference between a "religion" and a "philosophy" is itself a somewhat philosophical difference. I, someone who has lived in Buddhist-majority countries and study it for a living, have been informed that I was wrong, Buddhism is not a religion, it is a philosophy. At some point, you just have to throw up your hands and shrug. It's worth remembering that some of Christianity's greatest thinkers - Saint Augustine, Thomas of Aquinas, Boethius, etc. - are by definition philosophers. This is usually where the conversation ends for me: Buddhism has just as many logicians and Priests as Abrahamic religions.

That said, your question is a little bit more in depth so I'll try and address each of the points you've raised and then address your main question:

Buddhism sprung out of Hinduism, and it has a wide array of gods venerated and worshiped.

This is... technically not true. "Hinduism" isn't so much a religion like we'd consider Christianity and Judaism religions, but more of a complex of religions like Abrahamic faiths. The most popular forms of Hinduism today have their most pervasive elements sourced in far more recent centuries. Bhakti (the practice of devotion) for example, began in southern India at the end of the first millenium (Buddhism grew out of northern India). Vedanta (arguably the most popular and well known form of Hinduism today) began to pick up speed, mostly as an intellectual movement, but later expanding, about five centuries ago. Pretty much any form of Hinduism we have today will have roots and tendrils deep into history (every single one of them will source the literally timeless Vedas, more on that in a second) but the main point is salient: what we call "Hinduism" today, in any form, is not what Siddhartha Gautama, the Buddha, was responding to when he sat under the Banyan Tree 2500 years ago. To say that Buddhism "comes from" Hinduism is patently false.

More to the point, the most particular point where Buddhism and Hinduism diverge into completely different religions is that Hinduism reveres and holds sacred the Vedas, where Buddhism rejects them entirely. This is crucial, as the Vedas are Hinduism's most sacred scriptures (i.e. the ones with all the gods) and all of Hinduism's following scriptures (i.e. the Upanishads, the Puranas, etc.) all emerge out of Vedic philosophy. Buddhism's primary distinction is that it rejects the Vedas. And arguably, by extension, the gods.

Arguably.

Buddhists have a large pantheon of gods, as well as the fierce deities which destroy obstacles against Buddhists.

Neither of the articles which you posted are patently false, but they are sorely lacking in nuance and present local cults and single-use rituals as if they are universally "Buddhist." This is an unfortunate mistake that Buddhists make, not just on Wikipedia, but in publication format as well.

An easy give away on the "Buddhist deities" page is the list of names are all listen in Tibetan (i.e. Ksitigarbha is an Indian name, with its Tibetan equivalent listed next to it, "sa'i nying po"). This doesn't mean the beings listed on this page don't exist in other parts of the world, i.e. Japan or China, in fact there's a pretty good rule: if it's Indian, it probably exists in the mythologies of other parts of the Buddhist world. Take the Bodhisattva Avaloketishvara: in Tibetan he is considered among the most sacred Bodhisattva, often referred to as "the god of compassion," Chenrizi (Tib: spyan ras gzigs dbang phyug). In China and Korea, he takes a primarily female form as Guanyin.

The "Fierce Deities" page, however, is almost entirely Tantric Buddhism which is almost (almost) exclusive to India and Tibet. Tantric Buddhism gets... tricky, quickly to say the least. I'm not a tantric adept, so I'm not going to start expounding doctrine. But I can say with some authority that Tantric philosophy isn't necessarily supposed to be taken literally. This is something that has caused conflict in Tibet, with Tibetans being confused historically over how to interpret violent and sexual imagery that was prevalent in the Tantras (where these Wrathful Deities originate). Teachers, of whom Atisha is probably the most well known, informed the Tibetans that these were symbolic, not literal. The image of the yabyum is meant to be the union of wisdom and compassion. The image of the wrathful deity is meant to be the destruction of illusion, falsehood, and evil in the presence of truth. Later, there would exist Tantric Fundamentalists who would take these images to heart and wear pieces of corpses on their bodies and drink blood.

So while yes, these things are true and are a part of the constellation of Buddhism, it's worth looking into each one individually. There are few (or probably better yet no) scriptures that are universally Buddhist. While Avaloketishvara might be found in all Buddhist countries in some form, you will find that his treatment is vastly different from prayerful weeping in Tibet, to candle-lit offerings in Korea, to polite indifference in Thailand. Meanwhile, the vast majority of the wrathful gods (are not listed on that page because they) are local cults that predate Buddhism in some form, and their worshipers are cognizant that the gods are not a part of Buddhism, but tangential to it.

One worshiper in Bhutan put it pretty well in Christian Schicklgruber's article Gods and Sacred Mountains, "I would never dare ask the Buddha to keep my cows healthy or to protect me in war."

Buddhists also venerate Bodhisattva's, or people who have achieved enlightenment, and they have their own concepts of divine beings similar to angels known as Devas).

This is true. None of what I wrote above necessarily negates your point about Buddhism worshipping gods (not that that's my goal either). But the way Buddhists approach their gods, whether local or Indian in origin, are vastly different from the way that Christians, Muslims, or Jews would approach their God.

As I said before, many Buddhists will light a candle for Avaloketishvara at the temple, but won't do much else.

Plenty of Catholics will do that for the Virgin Mary, or St. <Insert Literally Any Name>. But it'd be wrong to then say that Catholics worshipped the Virgin or the Saints as Gods. It'd be heretical, in fact. On the page listing "Fierce Deities," (I keep stumbling over this term because the more commonplace term is "Wrathful Deities") they list the Four Guardian Kings as "Deities," which I suppose may be technically true, but these four statues usually grace the gateways of temples and monasteries but are never really worshiped like one might worship the Buddha, a Bodhisattva, or a local deity.

The problem really seems to be this term "deity."

"Bodhisattva" literally means "enlightened being." An "Arhat" literally means "Perfected one." None of these English translations even remotely carry the significance or the context that their Sanskrit equivalent has, so the default "Deity" is employed instead. Somewhat ironically, "deva" does literally mean "God" but in the hierarchy of beings you've listed, the Devas would be the lowest and least likely to be worshiped.

It's worth lingering on that point: what makes the Abrahamic God god? Usually three qualities are imposed: omniscience, omnipotence, and omnipresence. The Devas are none of this. They enjoy extreme pleasure and power for an extended period of time, but the Devas (assuming we can subsume the Wrathful Deities and Local Deities into their realm) are subject to the winds and fluctuations of Karma just like any other being and their time as gods will eventually come to an end.

The Bodhisattvas, as you said, are human beings who have achieved enlightenment. Neither by classification nor behavior, gods. Their goal is the ultimate enlightenment of everyone and everything they can reach.

To put it simply: just because Buddhism venerates certain beings and labels other beings (often ones with less veneration) as gods, doesn't really affect the theoism-icity of the religion.

cont'd.

This is also related, why are most Eastern religions called "philosophies" instead of religions? Buddhism, Confucianism, and Taoism are all religions with their own concepts of divinity and heaven, yet they are for some reason treated differently from paganism or Abrahamic religions.

Religion in China is a very complicated matter, and I think it's ultimately overly reductive to worry about whether these are philosophies or religions. However, the simple answer though is that they are treated differently from Abrahamic religions because they are different.

In China, the biggest religion in terms of adherents both now and for thousands of years has been what we call "Chinese Folk Religion," which is difficult to describe in a nutshell but has many of the characteristics that one would typically ascribe to a religion: afterlife, gods, worship, sacrifice, cosmic and natural order, the role of mankind in the universe, and so on.

For Confucianism and Taoism, some people might claim they are a "philosophy and not a religion" because both find their origins in texts that are not particularly religious. If you read any of the canon of Confucian or Taoist thought, you will find that the overall thrust of the texts is commentary on ethical behavior, what a person should do or understand, and how society ought to be organized. Taken individually, it is dubious to claim that any of the texts are primarily religious in nature. Of course they are different from what we would call modern philosophy - all the texts claim some kind of a priori knowledge without building up an axiomatic system of logic. As an example, Confucian texts reference the concept of "Heaven" as an abstract source of perfection and harmony, and reference divination practices.

Arguments against calling Confucianism a religion is that the canon lacks most of the characteristics of what most people would imagine a religion is: afterlife, origin of humanity, or requirement of belief. A Confucian gentleman is enjoined to take part in ritual, but as a matter of social harmony. Matteo Ricci, the famous Jesuit priest and missionary (and one of the first westerners to master the Chinese language) believed that Confucianism and Christianity were compatible, and in fact borrowed a lot of Confucian language in his effort to introduce the gospels into Chinese.

Taoism I think is more complicated because it encompasses both a liturgical tradition and a more philosophical tradition based on several canonical texts. An argument against calling Taoism a religion is that the first liturgical tradition involving Taoism (the Way of the Celestial Masters) did not come about until hundreds of years after Taoism began as a philosophy (sometime in the 4th century BCE vs 142 CE). I think that if someone must classify it as a religion, it cannot be considered an organized religion.

Buddhism has to be considered separately, because although it has had great influence on Chinese culture it has also been suppressed as a foreign influence during various points in history that are beyond the scope of a simple comment.

Ultimately however Chinese scholars since at least the 6th century CE have been writing about the concept of the "three Teachings" - Buddhism, Taoism, and Confucianism - as parts of a larger harmonious tradition, the core of which is Chinese Folk Religion. While Buddhism could be separated from this tradition and viewed as its own independent system in other countries, Taoism and especially Confucianism cannot really be excised from the syncretic folk religion without losing their religious aspects. In the end I think the argument over whether they are primarily religious or primarily philosophical is not particularly useful, but they do have a lot of characteristics that make it unwise to try to make a one-to-one comparison with an Abrahamic religion.

tl, dr: Taoism and especially Confucianism have no real religious characteristics of their own that weren't borrowed from the larger folk religion, and the differences between Taoism and Confucianism are mostly philosophical.