A Muslim killing someone who insults Mohammad, vigilante style, is part of Islam
https://sunnah.com/abudawud:4361
Book: Prescribed Punishments (Kitab Al-Hudud)\
Chapter: : The ruling regarding one who reviles the prophet (
A blind man had a slave-mother who used to abuse the Prophet (ﷺ) and disparage him. He forbade her but she did not stop. He rebuked her but she did not give up her habit. One night she began to slander the Prophet (ﷺ) and abuse him. So he took a dagger, placed it on her belly, pressed it, and killed her. A child who came between her legs was smeared with the blood that was there. When the morning came, the Prophet (ﷺ) was informed about it.
He assembled the people and said: I adjure by Allah the man who has done this action and I adjure him by my right to him that he should stand up. Jumping over the necks of the people and trembling the man stood up.
He sat before the Prophet (ﷺ) and said: Messenger of Allah! I am her master; she used to abuse you and disparage you. I forbade her, but she did not stop, and I rebuked her, but she did not abandon her habit. I have two sons like pearls from her, and she was my companion. Last night she began to abuse and disparage you. So I took a dagger, put it on her belly and pressed it till I killed her.
Thereupon the Prophet (ﷺ) said: Oh be witness, no retaliation is payable for her blood.
A Muslim killed his slave for insulting Mohammad. Mohammad ruled that there is no blood money/retaliation due.
If Islam comes from the Quran and Sunnah (Actions and words of Muhammad), then a Muslim killing a tiktoker today for cursing Mohammad can easily be argued as in line with Islam.