The Edinburgh South West MP was removed from her post as the SNP's justice and home affairs spokeswoman at Westminster, having come in for criticism over her stance on transgender issues.
She contacted police on Monday February 1 over a "vicious threat" to her personal safety after revealing she had been "sacked" in the reshuffle.
In her article she claimed that her belief that "women are adult human females" made her unpopular with some in the SNP, and said she was being targeted by "young men (...) who seem to have a problem with middle-aged lesbians who support women's sex-based rights".
Ms Cherry said: "The reasons for my sacking were not made clear but I was not surprised.
"For some time a small but vocal cohort of my SNP colleagues has engaged in performative histrionics redolent of the Salem witch trials.
"The question - do you believe or have you ever believed that women are adult human females? - is one I must answer in the affirmative, but it's not a response that is popular with some who have the ear of the leadership.
"It's frustrating because advocating for women's sex-based rights under the Equality Act, expressing concerns about self-identification of gender and opposing curtailment of free speech, are not evidence of transphobia."
On Thursday, police confirmed a 30-year-old man had been charged with a communications offence in connection with the incident.
She added: "Police Scotland came to take a statement and I filled them in on the background to these threats: an 18-month campaign of social media lies, smears and foul-mouthed abuse directed at me from a number of mainly young men within the party who seem to have a problem with middle-aged lesbians who support women's sex-based rights."
Ms Cherry went on to highlight what she described as "unprecedented" turmoil within her party, which has seen splits since the Alex Salmond harassment investigation.
The SNP has previously said she was removed from the front bench because of "unacceptable behaviour" - not because of her views.
Reporting by PA