One way self-proclaimed Buddhists identify themselves as such is by taking refuge in the Triple Gem of the Dharma, the Buddha, and the Sangha. Usually when a lay follower takes refuge they are advised to take a vow to follow the five precepts:
- to refrain from killing
- to refrain from stealing
- to refrain from lying
- to refrain from improper sexual conduct
- to refrain from consuming intoxicants
It is important to note that the decision to undertake these five precepts is completely voluntary. Moreover, it is not compulsory to take all five... many Buddhists only undertake some of these precepts while omitting others. Many Buddhists do not take the fifth precept of refraining from consuming intoxicants.
It is also important to note the scope of these precepts and that they too can be voluntarily widened or shortened. For instance, some will only take the first precept as vowing not to kill other human beings. Others will take the precept with all sentient beings in mind; vowing not to kill even an ant or a fly.
Lay followers are generally encouraged to take as many of the precepts and in as wide of scope as they can faithfully undertake. It is always possible to widen the scope or undertake more precepts at a later time.
Further, when one takes refuge in the three jewels, it is advised that one should give up taking ultimate refuge in a creator god or other religion. It is also advised that one should give up associations with people who would actively harm one's refuge by disparaging the Dharma for instance.
This does not mean that one is barred from following the practices of another religion where they are beneficial and non-contradictory!
Rather, it just means that one is advised not to take refuge in the Triple Gem while also believing in the salvation of a creator god. The reason is because these two are not generally compatible and will cause confusion when confronted with the necessary contradictions involved.
So to answer your question, I would say an Islamic country - for instance - should respect these precepts and allow non-majority Buddhists to follow them as well as take refuge in the Triple Gem. I would also say that the Islamic country should not ban the ability of the Buddhists to form Sangha communities and to pass around Dharma literature and actively practice their faith and religion.
The forming of Sangha communities (monks and nuns living in commune or in solitary areas) and the precepts that monks and nuns (voluntarily) undertake involve more proscribed precepts. And it is important to note that Dharma teaching and literature will also necessarily involve pointing out the contradictions between what Buddhists believe and what is implied by a creator god bestowing liberation. This is where I think it most likely that tension could be found between Buddhist rules/precepts/beliefs/practices and the rules of a dominant Islamic country. I do believe it's possible for the two to live in mutual respect and tolerance, but it will involve kind acts and giving the benefit of the doubt and respect for the views of others on both parts.