Is it possible to adhere to the practices and beliefs of both Buddhist and Christianity? What are the similarities and contrasts between Buddhism and Christianity? To what extent do they make it possible (or not) to practice in and hold the beliefs of both?
It is not possible to be both a Buddhist and a Christian because Buddhism teaches all things without exception are 'anatta' ('not-self') &amp; 'the elements' ('dhatu') as its core &amp; fundamental principle; where as Christianity includes 'self' in the form of Christ &amp; The Father as a core principle. 

In other words, Buddhism is strictly 'impersonal' where as Christianity is 'personal', where salvation is based on a personal relationship between the 'small-self' &amp; a personal god (Christ &amp; The Father). 

For example, Matthew 16:25 states:


  Whoever loses his life for My sake will find it.


Luke 23:42 states:


  Then he said, “Jesus, remember me when You come into Your kingdom!” And Jesus said to him, “Truly I tell you, today you will be with Me in
  Paradise.”…
  
  


Buddhism explains there are many types of liberation/salvation of mind (MN 43), which include liberation via loving-kindness &amp; liberation via emptiness of self, the later being the foremost &amp; unshakeable. 


  He keeps pervading above, below &amp; all around, everywhere &amp; in every respect the all-encompassing world with an awareness imbued with good
  will (loving-kindness): abundant, expansive, immeasurable, free from hostility, free
  from ill will... This is called the immeasurable mind-release.
  
  And what is the emptiness mind-release? There is the case where a monk, having gone into the wilderness, to the root of a tree, or
  into an empty dwelling, considers this: 'This is empty of self or of
  anything pertaining to self.'
  
  Now, to the extent that there is immeasurable mind-release, the unprovoked mind-release is declared the foremost. And this
  unprovoked mind-release is empty of passion, empty of aversion,
  empty of delusion. 
  
  MN 43


Christianity is merely liberation via loving-kindness where as Buddhism is liberation via emptiness of self. 



Also, Christianity teaches salvation is 'Eternal Life' where as Buddhism teaches salvation is 'dispassion' that occurs via the realisation of impermanence &amp; not-self. In other words, Christianity is a doctrine of 'Eternalism' (the belief a self exists after death), which is a wrong view in Buddhism; where as Buddhism is a doctrine of impermanence. 



In its most esoteric interpretation (which is rejected by most Christians), Christianity is 'mysticism' where as Buddhism is 'straightforward'. 

Jesus said he taught using parables to hide teachings &amp; the New Testament is replete with the language of metaphor, which results in most Christians being unable to discern between the literal &amp; metaphorical. 

Where as the Buddha taught straightforwardly &amp; plainly, with key terms explicitly defined. 



Also, Christianity is fatally connected to the Old Testament of Judaism, which allows killing in many circumstances, such as war &amp; heresy. This is why Christianity has had many Inquisitions. 



In conclusion, Buddhism states it is "impossible" for a person of right view to take refuge in another teacher, thus it is not possible to be both a Buddhist and a Christian.

Since Buddhism states: "‘It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise contemporaneously in one world-system", the view of Buddhism is those teachings of Jesus that are similar to Buddhism have their source in Buddhism. Therefore, the Buddha is the teacher &amp; Jesus is the student.


  He understands: ‘It is impossible, it cannot happen that a person possessing right view could acknowledge another teacher ― there is no
  such possibility.’ And he understands: ‘It is possible that an
  ordinary person might acknowledge another teacher ― there is such a
  possibility.’
  
  He understands: ‘It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise
  contemporaneously in one world-system ― there is no such possibility.’
  And he understands: ‘It is possible that one Accomplished One, a Fully
  Enlightened One, might arise in one world-system ― there is such a
  possibility.
  
  MN 115