Would it be frowned upon to say for example ぼく instead of 僕？Or わたし instead of 私？Is it just a stylistic choice or do these have to be in kanji?
This depends on the pronoun.
- Some casual first-person pronouns are almost always written in hiragana because there are no ways to write them in kanji in the first place: うち, わい, あたし
- Some stilted first-person pronouns are always written in kanji: 小生, 朕
- Many common first-person pronouns can be written both in kanji and in hiragana. Basically it's a matter of taste, but generally speaking, the more casual the situation is, the more frequently hiragana is used.
- Many adults choose to keep using わたし instead of 私. See: Why is 私 a sixth grade kanji?
- 僕 is not even a 教育漢字, but the majority of adults use kanji.
- 俺 is usually spelled with kanji, but おれ and オレ are not uncommon.
- 儂 is usually わし, but 儂 is not uncommon in novels.