If you are interpreting or translating a particular phrase, saying or sentence which goes against your religious beliefs, what would you do?

there are two possible positions on this issue; 1 in Translation, interpretation and narration you are not responsible for the statement.
so keep doing your job it will not harm your belief.
2nd and ideal is that if you have strong belief and you can challenge any thing even your job, then leave such projects which are against your beliefs

As a translator / interpreter your Job is to translate what is being said from one party to another, regardless of the content you're translating, It's unethical of me to deprive a party from hearing the other party's opinions.
I've worked as an interpreter for the CNN, Fox and other big news agencies, and one of the most important things I've learned about the ethics of the job is that journalists/translators should be neutral and their job is to report/translate not debate.
So I would highly recommend you to do it, and never to mix your opinions with your work.
Good Luck

i just translate it it's my job and no blame on me i am just a modem! only if this would lead to any kind of punishment for the speaker i notify him/her before translating!

This is just like working in interest banks, insurance companies, or taking interest loans ...and that debate on halal and haram.
I think, only the concerned Sheikhs are to decide on each case separately.

in this case you have two solutions:
1- you continue translation / interpretting the whole statement as it is without any modification without any remarks either written or spoken
2- which is the best solution you do your job as translating or intrpretting what ever statement you face and then you stated you opinion to bothe sides of the dialict

as a translater you need to put in your mind that you have to preduce a solid complet prodect and first of all you dont have the right to change any word from the text you are translating and when you get acroos a situation like this you gust keep translation becouse this is your job for example you are intterpetating in a confrens and the speaker side this things then you have to intterpet it and this your jop and you are the linke so you need to indore every situation

The main characteristic of the translator is honesty as the translator isn't the writer of the source language.

My purpose as a translator is to convey what is said in one language to the right (accurate) equivalent in an other language. A translator is not required to think of his belief while he is doing his work.

Whereas a translation adheres closely to the original with little room for license beyond the best rendering of a word or phrase, and an adaptation may depart wholly from the original, a transposition traces the source, but modifies it based on the transposer’s plan for the content and form. In terms of possible options open to the transposer, I can think of the following:

• Transposing the content
• Transposing the form
• Transposing the form and content
• Rendering narration as image or illustration or film or another form of media

Adapting the content, for instance, may range from modernizing it to altering it completely or even eliminating it. Adapting the form might involve simplifying or complicating sentences, restructuring sentences, eliminating sentences or shifting the perspective (from third to first person).