Most of the initiation methods I've come across as an intermediate practitioner mostly include rejecting Christianity or some other versions of that. But if someone who's not a Christian, like a Hindu, or Buddhist, would these initiations work for them?
Also, any good self initiation methods you would suggest?
I don't think they would have the same effect, no. I also don't believe this to be a 'norm' in initiation rituals.
Initiation is about passing on access to a current represented by a specific group. In the AA for example this is the 93 current or Thelemic current, the energies of new aeon and the HGA of the aspirant themselves which is the interface of the candidate that steps in as the representative of the God head. There is no antichristian elements in that ritual and it is more Graeco-Egyptian in its format.
The OTO initiation rituals do have some elements subverting christianity and traditional freemasonry, but this is because the majority of people who were in OTO at the time of Crowley would have been familiar with Christianity and freemasonry. It is therefore a mechanism to shock and release which has a magical effect. There is power in subverting norms, doing things differently, and some practitioners tap into this. For example in trad witchcraft there are rites in which one walks backwards anticlockwise around a church saying the lords prayer backwards. This raises power because it is subverting the norm, there is power in heresy, but you need to feel heretical whilst doing it!
The Golden Dawn rituals are also not about subverting Christianity, nor is Wicca. In fact the apostolic succession of Bishops within Christianity can be seen as an initiation as it is a passing down of power stemming back to St Peter, they are even consecrated with oil.
I don't believe you can self initiate. I believe it has to be done either by interaction and passing on a current by a person who has had the same done to them, or it is performed by the spirits themselves. I don't believe you can simply initiate yourself into something. This does not mean you cannot be initiated through working with the spirits, simply that it takes time and is not something that happens overnight.
Most initiations, early ones anyway, are about cleansing a candidate making them a vessel for spiritual force. In the rituals involving rejecting christianity this is more about releasing themselves from shackles they have experienced as a result of the abuses and soul smothering nature of the church. It is meant to cleanse some of that shame and negativity holding a person back. If a person does not have these feelings, then such a ritual will not have the same effect on them.