It is not rude as such, but unusual for strangers to talk on the shinkansen except to ask something specific like if it's okay to recline the seat (asked to the person sitting behind you.) Usually it's very quiet in there except for groups travelling together.
I live and work in Tokyo and take the shinkansen to and from Osaka about once a month. I am a visibly white woman but I don't have the usual apparel or luggage of a foreign tourist.
People take the shinkansen for the same reasons as a domestic plane flight. Some people are using it to take a fun and rare trip, others are commuting, some are going to weddings or funerals. It's my perception that most lone riders do not expect to talk with anyone, with the majority putting up some sort of barrier to conversation such as putting headphones on or closing their eyes. It would be rude to disrupt these people after they have already put up that barrier.
Otherwise, there is no harm in trying to talk to your seatmate, but I would test the waters first by saying hello and smiling when you sit down, then seeing whether they greet you back, just smile, or not even make eye contact.
Perhaps you could then ask them a question that gives them a chance to help you out. You could ask them which side of the train Mt. Fuji will appear on. How they answer will give you a clue if they want to talk more, and you can go from there.
I have ONCE in six years had a person sitting next to me spontaneously talk to me and we ended up productively chatting about where we are from, our jobs etc. for the whole trip back to Tokyo. He was a bubbly Osakan in line with the stereotype, and I felt he wasn't trying to pick me up but was just curious and wanted to fill the time. This was on the way back from the Obon summer holiday. He even gave me one of his many boxes of Horai pork buns as a thank you -- I guess he felt he could part with one. So you never know!