Swastika is religious symbol in India and many countries don't find it offensive but due to Nazi connections, will a traveler will get in trouble if he carries anything with the swastika symbol in the USA? Like a T-shirt, Tattoo or religious book with that logo? Do I need to hide it, or avoid even carrying it?
It is not illegal to display a swastika in the US; however, the symbol is generally understood in the US to be a symbol of Nazism and displaying it publicly is likely to be extremely hurtful to those around you (perhaps in particular members of groups targeted by Nazis), not to mention earn you significant unwanted attention. If it is on a religious book and it is clear that it is a religious symbol unrelated to the Nazi party, then that is more likely to be OK. I would definitely avoid wearing it on a t-shirt or displaying a swastika tattoo.
Source: I am a US resident.
I mostly agree with @ajd's answer, and it'll depend a bit on where in the country you are. While I hate stereotyping, in the US it's not a bad starting point.
T-shirts and apparel with a swastika is almost certain to get you negative attention, especially in more liberal parts of the country, though one might think that more liberal areas would be more likely to understand the difference. In heavily conservative areas, you're more likely to be harassed for being Indian than for a swastika (yes, I've seen it happen). I know it sounds like I'm bashing my country, but this is mostly a worst-case scenario type of thing - better to be prepared and understand than not. :)
The current socio-political environment in the US and the increase in white supremacist activity definitely puts a damper on this particular religious freedom. It's not illegal, and you won't be imprisoned or fined, but I'd be concerned about your safety and well-being.
If you happen to be coming to Michigan, let me know. We have a pretty heavy Indian population here. I can ask a few friends for advice, if they have any, on this particular issue. :)
The public display of Nazi flags is protected by the First Amendment to the United States Constitution which, affirmed by the Supreme Court case Texas v. Johnson, guarantees the right to freedom of speech. (sources)
It's also used by some political or social groups for rallies. Saying that, to most people it'll be associated with Naziism, despite the original orientation/meanings that were co-opted.
Most people are likely to just give it a look and form an impression of you that you might not appreciate, but aren't likely to engage. Some however, might take more of an issue with it.
Depends a ton on the context. People from India run the gamut in skin color. If you have light colored skin, people might associate you with white supremacists who openly carry Nazi symbols. A known white nationalist doing an interview was openly assaulted on the street (it's an isolated incident but some people felt it was justified). If you are darker skinned, that association is much less likely to be made.
Books are unlikely to get you noticed in this fashion, especially since you don't have to display them. Clothing certainly will and tattoos are even more closely associated with it.
The term "swastika" includes a wide variety of symbols. Something like this or this is much less likely to be perceived as being a Nazi swastika than is something like this. It also helps if it's incorporated into a very-not-German design, such as this.
Also, while Germany is, to my understanding, sensitive to any use of a swastika in any context, there are many contexts in the US where it is acceptable. For instance, the book The Man in The High Castle is set in a universe where Japan and Germany occupy the US, and its cover depicts the Japanese and Nazi Germany flags. So a book with a swastika, even if it's perceived to be a Nazi swastika, would not necessarily be perceived as being pro-Nazi.
So, to summarize: how it's received will the depend on the type of swastika, the context, the viewer, and whether you have other attributes associated with Nazism (e.g., blond, blue eyes, skinhead haircut, etc.).
There are no laws specifically against Nazi symbols or Nazi paraphenalia (clothing, medals, etc.) in the United States, and there are NO laws against religious symbols, even if they are swastikas. Airport authorities will not give you any trouble, and if a police officer or customs officer asks, simply inform them it is a religious symbol.
That said, many places, like university campuses or workplaces, have regulations or policies against 'offending people', so people who don't understand that the swastika is an ancient religious symbol used in many cultures might complain and make trouble for you. In that case, prove your swastikas are religious with a quick internet search on your phone, demand that they respect your right to religious freedom, and then accuse them of racism if they don't stop bothering you. They have NO RIGHT to bother you because of your religion.
If you look like a person from India, and your swastika looks Eastern and not Nazi, I doubt people will bother you unless you are somewhere extremists congregate, like university campuses. If people try to pressure you into not wearing your religious symbols, it could be a violation of your civil rights.