To investigate the incest allegations of Mushoku Tensei, I used breeder software to calculate the characters' inbreedability rates.
Of all the characters, only 7 are inbred.
Since inbreedability rate below 5% is considered safe then only 3 characters are dangerously inbred.
Them being Nel and Jill Britts with 6.2% alongside Leroy Greyrat with 7.0%. These three could develop problems if they don't clean their bloodlines.
Veredict: Incest not that prevalent to warrant such slander