I have little doubt that this new law will be weaponised by trans rights activists to try to silence, and worse still, criminalise women who do not share their beliefs.
A cursory look at social media shows that some of these activists already have one high profile woman in Scotland in their sights. Experience shows that working class women will also be targeted.
There is no right not be offended but the muddled discourse about these issues currently in the public domain does not make that clear.

[Nicola] Sturgeon remains blinkered: she has ignored female victims of male violence, treated the concerns of the UN special rapporteur dismissively and failed to listen to young people who received appalling care from NHS Scotland and now regret their transition. Her implausible mantra remains that no man will abuse the system, women's rights are not affected and evidence reviewed by an English paediatrician has no relevance to Scottish children. Scottish Labour could still try to amend the bill to make clear that a GRC does not change someone’s sex for the purposes of the Equality Act.
But the most likely outcome is that Sturgeon, a self-professed feminist and nationalist, will leave the door wide open for a Conservative government in Westminster to step in to protect Scottish women, by updating the Equality Act to clarify its sex-based protections for women apply only to those who are biologically female.

[M]ales who wish to identify as women will be offered additional protections under the law; but those born female will not benefit in the same way. Of course, trans-identified people should be protected from abuse and discrimination. But why not women too? Does the SNP think the minority of individuals who choose to identify as transgender are much more at risk than women and girls? Women suffer disproportionally as victims of rape, domestic abuse, FGM, child marriage, and femicide around the world, yet in Scotland this seems to count for little.

To many people, it will look like this convicted rapist has gamed the system in order to try and garner sympathy, and to end up in a women's prison. And I think a lot of people will be shocked by that.
So I think we should be talking about these cases. And women in prison are very vulnerable. Many women in prison have themselves been abused, and have suffered injuries over the years. ... But the point about human rights is that they're universal, and they apply to everyone. So I'm very concerned about the safety of women prisoners, with whom a convicted rapist has been placed.
And under Scots law, the crime of rape can only be committed by somebody with a penis, and that's a man. And I think we should call out what's happened here.

The Scottish Bill tears up the UK’s criteria for awarding a gender recognition certificate based on medical assessment, and allows anyone to get a GRC based on a declaration, with no medical treatments or safeguards.
This means there will be many more people able to get a certificate, and organisations will never be able to feel confident excluding someone who is clearly male from female-only spaces and services.
A key question for the UK Government is whether they will accept people who have been through the Scottish system but were born in England and Wales to change the sex on their birth certificate. Scotland would in effect act like a 'haven' of light regulation that would then spill out across the UK.
For schools there would be huge problems. Single-sex schools are allowed by law, but now schools would face having to admit a child of the opposite sex, and would be threatened with criminal penalties if teachers and staff 'disclose' the child’s actual sex to other staff, pupils or parents.
The UK Government does not have to accept this outcome. It should refer the Bill to the Supreme Court and make sure that the Scottish Parliament only legislates within its own domain, and does not ignore women’s rights and child safeguarding.

Significant national legislation relating to rape, sexual abuse, domestic violence, early or forced marriage, discrimination in inheritance, marriage and property rights, among others, have been enacted to protect women’s rights, empower them in society and enhance their mental health and well-being.

As a woman, I fully understand the threats to dignity and safety that the Bill poses, because it will change the social contract. In this country, we recognise that in toilets, changing rooms and public spaces, there are areas where only women are allowed.
In a restaurant recently, I had an experience where a man dressed as a woman walked into the toilets where I was on my own. He stood behind me and stared at me in the mirror, looking me in the eye. I have no idea whether he intended me any harm, but my evolved instinct as a woman was to be frightened, because unlike in almost any other species, women are far less powerful than men and we cannot defend ourselves. [Interruption.] No, it is a fact. The difference in strength between men and women is phenomenal, which is why we have separate sex categories for sport. Women are evolved to be wary of men in intimate spaces, which is why we have single-sex spaces and why they must continue to exist for the safety and privacy of women. The Bill threatens that social contract.

It may infuriate Nicola Sturgeon, but it seems that JK Rowling's political judgment is superior: the Gender Recognition Reform (Scotland) Bill will be Sturgeon's poll tax. Sturgeon is not in control of this. She allied herself with zealots, ignored public anxieties, denied biology, produced a bill that most can see is deeply flawed, rejected sensible amendments such as barring sex offenders from self-identification, and cannot hide from the people that predatory males, if the bill becomes law, can manipulate it to invade women’s safe spaces. The recent rapist case will not be the only one that will haunt her.

The [Scottish] government said its proposal will not diminish the rights of women.
However, its own draft equality impact assessment evidenced this by citing Bristol University research which . . . suggests that a woman catching sight of a male body in a changing room should be no more distressing than seeing another woman with a mastectomy. Does the government regret citing this research, and do they agree that the comparison is insulting to breast cancer survivors?

We need better laws to protect women and girls

Make no mistake, if Roe v. Wade is overturned, women will be harmed and some will die. It happened before Roe became the law of the land and it will happen again, particularly since this decision will harm low-income and at-risk women more than anyone

I cannot think of a system of law that dehumanizes & degrades women more than Islamic Law.

New family law can end violence against women.

This bill, if passed into law, will serve as a deterrent to those who will take advantage of the poverty situation in order to profit from selling our women and children. This is one of the most repulsive crimes in society today, and we must not allow our women and children to fall prey to these vultures.