Many peoples says don't offer salat/prayer in a Shiite mosque if you are Sunni Muslim.
Is it impermissible to pray in a Shiite mosque?
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Saying prayers in mosque of Shia and Sunni is totally unrestricted. Even saying prayers in church is allowed (if it has no danger for your religion).
Also the whole world is created by Allah. No one can restrict from for praying to him by building anything.
But it's better to pray to Allah in a mosque because of hadith from prophet Mohammad(صلى الله عليه وسلم):
Mosques are houses of Allah in our world.
and another hadith from prophet that says:
Mosque is home of every Muslim.
So there is no difference between Shia and Sunni in this hadith.
(Sorry for no source for hadith. I couldn't find any English source for them.)