Can you be deported, exiled, or prevented from entering Japan after naturalization?

No. When you ask somebody what "naturalization" to Japanese gets you, the first answers off the top of their head are "the right to vote" or "the right to hold office", and they will usually follow that up with "these aren't things you do very often, so naturalization really doesn't give you much over permanent residency"

However, there is one right that you get to exercise every day: the right to enter and live and work in Japan at will.

When you are a foreign resident of Japan you have "permission to be in Japan". When you are a Japanese national, you have the right to be in Japan."

Contrary to popular belief, "permanent resident" SoR (永住者在留資格 {eijūsha zairyū shikaku}) does not give you the right to be in Japan, nor is it a promised to be truly "permanent" — either by the foreign resident or by the State of Japan. Permanent Resident Status, just like other "non-permanent" legal foreign resident statuses, can be lost, revoked, and taken away under certain circumstances — either due to one's own actions (being deported or letting one's "permanent" status of residence "expire" due to being outside of Japan for too long) or due to no fault of your own (change in immigration policy via the legislature).

If you're a Japanese national, however, you have what is often called in other countries (such as the United Kingdom), an irrevocable "right of abode" (ROA).

You do not lose the ability to enter Japan even if you lose your Japanese passport and/or your identification while overseas (obviously there must be some way to verify you're Japanese via official documentation on file with the Government of Japan, however). Japan's Ministry of Justice immigration site explains the Immigration Control and Refugee Recognition Act, Section 7, Articles 60 & 61 (日本人の出国及び帰国／入管法第７章第６０〜６１条 {Nihonjin no shukkoku oyobi kikoku / nyūkan-hō dai-7-shō dai-60~61-jō}):

  日本人が帰国することは，国民が当然に有する権利として解されています。このような権利を有する日本人の帰国を外国人の入国と同様の手続とすることは適当でないので，入管法は日本人の帰国手続について外国人の入国手続とは別な方法を規定しています。

  日本人の帰国の手続は，入国審査官が帰国を確認し，原則として旅券に帰国の証印をすることになっていますが，やむを得ない事情により旅券を所持していない場合には，帰国証明書を交付することによって行うと規定されています。これは，たとえ旅券を所持することがなくても日本の国籍を有することを証する文書を所持するなどして，日本人であることが確認されれば，帰国することに支障がないことを明らかにしたものです。

Translated:

The ability for a Japanese to return to Japan is understood to be an obvious right for all legal nationals. This is why the procedures for a Japanese entering the country are different from the procedures that a non-Japanese uses for entering Japan.

The procedures for a Japanese to return to Japan through immigration are facilitated via using a passport as proof of one's nationality, however in extenuating circumstances where one is not in possession of a Japanese passport, a certificate allowing return [such as a Travel Document for Return to Japan] will be issued to allow one to return without hindrance, after their Japanese nationality has been confirmed through other means [such as a Japanese driver's license].

I've actually experienced this situation personally first hand: I got into a situation where I left Japan without possessing a Japanese passport yet. After confirming that I had Japanese nationality, immigration let me back in the country despite me not having proper Japanese papers!

In addition to the immigration law, there are two other laws that guarantee a Japanese national come and go and live and stay in Japan as they please. The first is the Japanese Constitution, Article 22:

• Every person shall have freedom to choose and change his residence and to choose his occupation to the extent that it does not interfere with the public welfare.
• Freedom of all persons to move to a foreign country and to divest themselves of their nationality shall be inviolate.

The second is Article 13 of the UDHR (which is translated to Japanese), which defines the phrases "human right" and "fundamental freedoms" that are used in the UN Charter, of which Japan is a member:

1. Everyone has the right to freedom of movement and residence within the borders of each state.
2. Everyone has the right to leave any country, including his own, and to return to his country.

Of course, just because a naturalized person can unconditionally enter Japan at any time, no matter what they've done (for example, an illegal activity), unlike a non-Japanese, does not mean they're free from consequences of your actions, either done within Japan or done overseas.

For crimes and misdemeanors, Japan can fine you. It can imprison you. It can even execute you. But it you're a Japanese national, they can't deport or banish you.