Hell, it's even one of the "Basic Points Unifying the Theravada and Mahayana". If it wasn't important I really doubt it would make the list:
Basic Points Unifying the Therav
It would be intellectually dishonest to remove this document (Basic Points of Unity) out of its native context, and to present it as a list of things a person must adopt to be a Buddhist.
The context of these unifying points is that Theravada Buddhism and Mahayana Buddhism spent several centuries in sectarian feuds with each other over which school is the "True" Buddhism.
There was a time when Mahayana referred to Theravada Buddhism derogatorily as Hinayana (the minor/lesser vehicle).
On the Theravada side, "we" don't recognize any of their sutras as being genuine teachings of Buddha. "We" also don't recognize their monks as being genuine. And "we" certainly don't recognize their nuns as being genuine, since in the Theravada tradition, the nun lineage went extinct a very long time ago.
The fact that this list even exists is pitiful and shows that even Buddhism is not free from the stupidity of sectarian politics.
A group of monks from both sides in the 60s got tired of the stupidity and tried to find common grounds to end the centuries long feud.
The list you provided is nothing more. It is a list of views both sides can at least agree on; a truce, if you will. It is not a list or things a person must obey or agree with to be a Buddhist proper.
This list in noway supersede what the Buddha taught regarding how a person becomes a "Buddhist" (an Upasaka/Upasika).
Pursuant of the Tipitaka, as per the Buddha himself, a human being only needs three requirements to be a "Buddhist" aka an Upasaka (male) or Upasika (female).
The three requirements are as follows:
1) Seek refuge in Buddha: Buddham saranam gecchami (I go to the Buddha as my refuge.)
2) Seek refuge in Dhamma: Dhammam saranam gecchami (I go to the Dhamma as my refuge.)
3) Seek refuge in Sangha: Sangham saranam gecchami (I go to the Sansha as my refuge.)
Notice that the belief or rejection of a god/creator is not one of the Three Jewels.
The many responses in this thread only serves to obfuscate the simplicity of (Theravada) Buddhism:
So long as a person takes refuge in the 3 Jewels they are to the Buddha, "Buddhists" in good standing.
Besides the Three Jewels a fellow wayfarer of the Way of Buddha can follow the Pancha Sila (5 Precepts) if they want to take their Buddhism up a devout notch.
The belief in or rejection of God also is not a part of the Pancha Sila. Neither is it a part of the some 200 precepts a monk must follow.
To seek refuge in Buddha does not mean that one believes him to be some infallible religious prophet or savior. He is simply a teacher. One person who has found a way to Sambuddhi: Self-Enlightenment. And he created a Way whereby any other person can in their own time and season manifest that same Self-Enlightenment. Sambuddhi has nothing soever to do with the rejection or acceptance of gods.
To seek refuge in Dhamma doesn't mean one blindly accepts everything and every word ascribed to the Buddha. Dhamma must be observable and testable.
To seek refuge in the Sangha means two things. That (1) if you can't find an answer to something on your own, you can go to the Bhikkhusangha (the order of monks) and ask for their opinions; and (2) that you can go to the Ariyasangha (the collective noun for all fellow Buddhists) and ask them for their opinions. The point here is that you go to a LIVING source, as opposed to going to dead letters and some list of points.
Thirza Fallen in her OP said she liked Buddhism but believes in God, and wanted to know if she can merge the two. The simple answer is: Yes you can, per the Buddha's words himself, and also per practice.
The fact is Thirza, there is no such thing as "pure" Buddhism
on a living cultural level. I will try and explain.
In the Southern Buddhism found in Thailand (I'm ethnically Thai), Laos, and Cambodia, the Buddhism there is merges with the more ancient Brahmanism.
Up north in China, Bodhidharma merged Buddhism with Taoism along time ago to come up with Chan Buddhism. In Japan Bodhidharma merged Buddhism with the local "Shintoism" and Zen came into being, which is a form of Chan. In Tibet the native people's Bon was merged with Buddhism and Vajrayana Buddhism was born.
In Buddhism jargon, this "merging" of Buddhism with other ways, is called an Upaya. It is a word most Westerners who study Buddhism don't pay much mind to. In the Tipitaka the Buddha says that one can use any Upaya so long as it manifests the end result of a person becoming a Buddhist. If you want to know more about upaya and what it is, you can research it.
Only in written text (in theory) is Buddhism "pure." This is a great divide between the Western mind and the Eastern mind. The Western mind puts the written text up on a golden platter. After centuries of being told that the written text of the Bible is the law, and the written text of colleges are where wisdom and knowledge is found, this is not surprising.
In the Eastern mind, Culture and Cultural Praxis is what is important and is what teaches. You/we get our Buddhism not from books or written texts, but from living sources. From parents, grandparents, neighbors, friends, monks, cultural icons, and so on. Unlike dead letters and written text, a living culture evolves and changes. And so in Southeast Asia, and up north, a living Buddhist culture evolves and grows over time. Asian cultures have had at least 1000 years of exposure to Buddhism to evolve. And so, over time, there will be a natural/gradual merger of Buddhism with native traditions.
As long as the upaya produces the end result of the person seeking refuge in the Three Jewels, the upaya is acceptable.
Just to breifly explain in practical terms what an upaya is:
The Catholic Church is good at "upaya-ing." They go into a new civilization of native Americans in South America. These natives have their own culture and set of gods. And so the Church will make those local gods into "Saints." This helps bring in the locals into the faith proper.
Mahayana Buddhism in practice is also good at this. "Saints" in Mahayana Buddhism are called "Bodhisattvas."
There are two "bodhisattva" in Chinese Buddhism worth mentioning. If you are a Chinese Buddhist, these two are present in your Buddhism and in your temples. My grandparents are Chinese.
The first Bodhisattva is Kwan Yin, and the second is one we call "Preah Gachai" aka the "Fat Buddha."
The reality is that before Buddhism was brought to China, Kwan Yin and the "Fat Buddha" were local gods of the natives. Kwan Yin was a Taoist "goddess" before she was a Mahayana "saint." The "fat Buddha" was the local animist god of the fecund earth spirit/father, corpulent and abundant, before he was made into a "Buddhist" "Bodhisattva."
Tibetan Buddhism is even better at this upaya stuff. Their Buddhism is filled with local Bon Po gods and spirit beings.
So if these other forms of Buddhism can "merge" Buddhism with things, and if people here regard Mahayana and Vajrayana as genuine schools of Buddhism regardless of the upaya and mixing, why can't you utilize Buddhism and its practices on your own terms and in your own way?
We are now even witnessing the creation (gradual birth) of a new yana of Buddhism, which the West is creating. This Buddhism is being merged with Western science, Western 'rationalism,' and with Western atheism/materialism. If merging Buddhism with science works to bring Westerners to take refuge in the Three Jewels, than it is acceptable.
The Way in and of itself is not important, in Buddhism it is the end destination that is important. What kind of car (vehicle/yana) you drive to get to that end destination is irrelevant, as long as it gets you there