Right Wing Authoritarianism has long been part of TERf ideology. In a comment worthy of Orwell, Janice Raymond said:

“Feminists must go beyond choice and consent as a standard for women's freedom.”

Their version of 'feminism' was not about improving women's lives, freedom, giving them more choice in their lives. It was to create a layer under the Patriarchy, where the anointed few 'feminists' ruled women's lives on behalf of it.

Think of nunneries in the Catholic church.

Where nun's lives are brutally controlled by women...on behalf of the male controlled church.

Attwood noted this convergence in beliefs, hence Gilead.

It should be no surprise given the Catholic backgrounds of the original (and even later) TERfs, Raymond was an ex nun, Daly a Catholic theologian.

The church itself noted this convergence in beliefs (see pages 11-13): https://philarchive.org/archive/ROWFFT 

There is no concept of human rights, of democracy, of freedom of choice, of states ran on secular beliefs, in either of the (closely related) ideologies. Rather a small elite would make the decisions for women and impose them.

Their opposition to Patriararchy was never about ending it, rather it was this 'elite' wanted their place in it. They wanted to be the Mother Superiors and quite happy to be under male priests, as long as they could 'influence' them.

Even the catch cry 'abolish gender' was never about actually doing that, it was to impose their idea of gender, which was fundamentally based on winding back the 'sexual revolution' for women, a return to 'chastity' and 'PiV sex for breeding only'.

Hence their concept of 'political lesbianism', which was really just akin to nun's chasteness and their 'marriage to Jesus'. A sexless women only 'nirvana', where women abstained from sex with men and had a wee kiss and cuddle now and then with other women....but not actually sex

So they offered only 2 options to women:

(a) Marriage to a man, having children and live directly under patriarchal rules.
(b) Live in a women's community and live indirectly under patriarchal rules, as interpreted by 'elite' women.

From that follow all of their other beliefs which, no surprise, were also just rewarmed Catholic 'natural law':
Given women's total inferiority to men, their only point of power was gatekeeping PiV sex and having children, thus any competition to that took away power from women

Thus they were against sex outside marriage, (most if not all) contraception, easy abortion (eg RU-486 and abortion clinics), IVF, sex workers, porn and so on.

And of course trans women. And, never forget, sexual lesbians.

This of course also appealed to Right Wing Women. They were the women choosing option (a), thus their investment in patriarchy that enshrined their power base...control over sex and child birth.

To them other women who do not conform to this are existential enemies.

Hence today's 'gender critical feminists' (GCF) who are an uneasy mix of good old right wing women and some (not many) old style TERfs alongside the male dominated 'christian' right wing.
When you look at their ideologies in detail they are the same (with a few words changed).

We see all this in just about every Twitter (etc) exchange with GCFs, the same beliefs (with, as usual, huge doses of hypocrisy) the same gatekeeping of other women and of sex, the same deep belief in women's inferiority where their only power comes from their vagina and womb.

And the perverse belief that the only 'good men' are 'masculine', right wing, patriarchal ones ...enshrined in their repeated statement:
'Right wing men want private ownership of women, left wing men want public ownership'...thus right wing men are the 'least worst' option.

And that right wing men can be trusted, while those 'deceptive' left wing men cannot be.

With the only other option for women being the 'nunnery'.... and the new 'nuns habit', a sort of soft butch, sexless, non feminine uniform.

And their supposed gender nonconformity has to be seen in that light. They are not rejecting gender so much as rejecting sexuality, 'femininity' being seen of as a male invention to make women more sexually appealing to them.

Hence their hatred of NB people and androgyny.

Thus how they are quite happy for women who choose option (a) to be 'feminine', but those who choose (b) to have to be their idea of 'sexless'.

Hence why they always hammer trans women for 'conforming to gender stereotypes', but never cis women who do it.

They believe that women who choose option (a) (trad wives) have to do that, that their 'conformance to gender stereotypes' is a supposed 'source of power' for them, a way of 'influencing' and (importantly) keeping their men.

Oh sure they want more women joining their side and following their version of gender conformity, but they are realistic enough to know that few will...and they are as invested in keeping that system going as do the 'trad wives'.

Let's not forget this and that Janice Raymond advocated conversion therapy for trans women. https://twitter.com/LisaTMullin/status/1197987970315255808