I wanted to ask that as per ayatollah Sistani it is not permissible based on compulsory precaution.

I am a married male and sought permission from my wife and she said you permitted but don’t come to me in bed.

So with her approval and as per ayatollah sistani, can I do mutah with a Christian ?

And after I have done mutah with a Christian, I can still visit my permanent wife on bed right ?

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Temporary marriage with Christian woman with the permission of a Muslim woman is not permissible on the precautionary basis according to the opinion of Sayyid al-Sistani, but, it is possible to refer the matter to others who say that it is permissible.
In any case, you can refer to your Muslim wife, as your marriage to a Christian – if we say it is permissible – does not forbid your Muslim wife to you, and she has no right to prevent you from having sex with her even if you marry without her permission.