Being a Buddhist is not about what one believes, as may be the case in traditional religious "faiths." Whether or not one is a Buddhist is about what one does and what one wants. Principally, in terms of action, does a person go for guidance (sarana) to the:
- Enlightened One
- Buddhist Teachings (the Dharma)
- Community of Enlightened-Disciples (arya-sangha)
The question of whether or not one is a "good" Buddhist is another matter altogether. One may ask of oneself, do I even attempt to maintain the Five Precepts?
- To abstain from killing living beings
- To abstain from taking what is not freely given
- To abstain from misconduct with regard to sex and sensuality
- To abstain from false speech (perjury and divisive, harsh, and impertinent talk)
- To abstain from intoxicants that are the basis for transgressing these precepts
The Precepts have a short (not killing, stealing, sexually-misconducting, lying, or drugging oneself) and long form. The long or more detailed form is spelled out in the Numerical Discourses of the Buddha, Book of the Tens, Discourse 206 (AN X 206). Its contents are a frequent topic of discussion at WQ.
For instance, what constitutes "sexual misconduct"? It's spelled out by the Buddha and not as open to interpretation as people often make out. It does not preclude one from having sex; it precludes hurting people in the process. See "The Extinction of Karma" (AN X 206). What is "lying"? Does it include fibbing or just perjury? Shouldn't we all be celibate and constantly engaged in Noble Silence?
Buddhism is not about a rigid, absolutist morality. Guidelines vary and they very much make sense -- until they're abstracted into simple forms and formulas that are (to Westerners) mindlessly recited.
Eastern Buddhists tend to know the details. So they recite patterned formulas as reminders, crib notes if you will. The same is true of discourses (sutras), which have detailed exegeses, but which are simplified and standardized to make them more memorable and general. They are tightly packed and not meant for literal interpretation. The Buddha did not use words so much as he used terminology. Without being familiar with the technical term (a difficulty compounded by rough translations), one is left with the words. And we know the words. So we think we know the meaning of the Dharma (the Buddha's teachings). The Buddha praised wide learning.
Finally, what does one want? One is a Buddhist if one wants to be. Otherwise, anyone who inquired about the vision of the Truth handed down as "Buddhism" would be seeking guidance. And any upstanding person with a predilection for basic virtue (since the Buddha did not invent the Five Precepts, nor was he unique in realizing that conduct affects states of mind, leading to calm and clarity or distress and distraction.
Moreover, Buddhism is the Path to enlightenment (liberating realization of the Four Noble Truths) and nirvana (liberation in this very life from all suffering). Perhaps most people want rebirth in heavenly realms or better conditions here and now or in other future lives here. These are legitimate goals, and they are achievable. But the unique teachings of fully Awakened Ones is towards that grand and final accomplishment of doing all that is good, neglecting all that is harmful, and seeing the truth directly.
In summary, of course you can be a Buddhist and any other religion you like -- as far as Buddhism is concerned. Not that monks have not misguidedly tried to make it an all-or-nothing proposition from time to time in history and at the climactic ending of some traditional sutras. The Buddha's position was always one of free inquiry.
However, your religion (and/or religions) may differ. It may not accept divided attention or allegiance. Warm regard for anyone but the Supreme Being and His prophet -- be it the Jewish ascetic Jesus (Y'shua son of Yusef and Miriam) in the case of YHWH or the Islamic Mohammad in the case of Allah -- could get you thrown out of the bishop's seat in the Church of England.
These are the three world-religions (Islam, Christianity, and Buddhism). Less universal creeds tend to be more polarizing, whereas more spiritual traditions tend to be less dogmatic. Therefore, your mileage may vary.
Whatever the case, whatever your choice (whether you make it or it is made for you), you can still benefit from Buddhism the way college students limiting themselves to a single major nevertheless benefit from wide and broad learning.