As a Christian, would it be considered rude of me to..?

Pray and worship at other religious..."centers" despite not being of their faith?

Like, I'm Christian, confirmed Lutheran, though I don't practice it but I have the background of being one.

Say I were to go to Japan and visit a shrine. Would it be okay for me to pray at one despite not being Shinto? Would it be considered a good gesture to follow in their faith for the time that I'm there or would it be seen as rude since I don't wholeheartedly believe in it (what they would probably assume) and am not as well-versed in it as they are? Same as if I were to visit a mosque or a Hindu temple or a synagogue. Would it be alright? I've always wanted to experience being in these different places but have always been unsure if it would be rude or not.

I mean, I have been in a Mormon church twice, but since it's still technically Christian you just have to alter what you do a tiny bit, like folding your arms instead of clasping your hands when praying.

Any input or opinions would be nice.