Depends what you mean by "blurring the lines of the patriarchy".
I think it helps to conceal patriarchy, which is deeply unhelpful to women.
Let's be very clear. Identifying as a member of an oppressed class is not the same as actually being a member of that oppressed class.
In any social justice movement, you identify your oppressed class by reference to a particular characteristic which those people share, you make a case that they are oppressed because of that characteristic, and you propose that they have a need for specific rights and protections because of it.
So, if your oppressed class is gay people, the characteristic those people share is that they are same sex attracted. They have historically been oppressed because of that characteristic, which can be evidenced due to the fact that until very recently they did not have equal marriage rights even in modern western countries, in many parts of the world they still do not have these rights and in some parts of the world their consensual sexual activities are actually criminalised. The need they have is equal rights to heterosexual people, and a protection from the abuse, harassment and discrimination they still suffer as a result of their sexuality.
If your oppressed class is people of colour, the characteristic they share is that they are not white. In many parts of the world they have been oppressed by white people, which we see historically with slavery and apartheid, and today in modern western countries where people from certain ethnicities, particularly black and Hispanic people in the US, are more likely to live in poverty, more likely to be shot by the police, more likely to go to jail, more likely to die in childbirth. They clearly have a need for protection against discrimination.
If your oppressed class is women, the characteristic they share is that they are female, i.e. the childbearing sex. They have historically been oppressed by men, who are able to physically overpower women and use them as sex objects and birthing vessels. Men have taken advantage of the fact that a large part of women's lives is taken up with pregnancy and childbearing to organise society in a way that benefits men and disadvantages women, from denying women the right to vote and own property, to more subtle forms of discrimination that still exist today. So women have a specific need for protection from oppression and discrimination by men specifically and society in general.
There are, of course, other oppressed classes to the ones listed above, such as disabled people, and the same principles apply.
Intersectional feminism, incidentally, was supposed to focus on women who are not merely oppressed because they are women, but are also on other axes of oppression such as being black, same sex attracted, disabled and so on.
Trans people are an oppressed class, although there is a slight difference in that it is a class they are in on the basis of their own, subjectively experienced identity, rather on the basis of tangible, undeniable, inescapable, unalterable and undisguisable features such as sex or ethnicity. They still suffer from discrimination on the basis of being trans, and should be entitled to protection.
The problem is that trans women, in particular, may be oppressed because they are trans, but they are not oppressed because they are women. They do not share any relevant characteristics with women. Or even any irrelevant ones, for that matter. They do not suffer the same discrimination that women do, in the same way or for the same reasons. The discrimination that women suffer is because we are members of the childbearing sex who are exploited, to a greater or lesser degree all over the world and at all times in human history, for our reproductive labour.
Redefining women to include male people, who are not exploited for their reproductive labour and who have not suffered any historical sex-based discrimination such as being denied the right to vote or own property, obscures the reasons for and the effects of sex based discrimination against women.
If we are no longer allowed to name ourselves and what we are, i.e. members of the childbearing sex, because we must be redefined to include male people, we can no longer effectively fight against our own oppression. And the people who wish to prevent us from doing that are members of the same group of people who have historically oppressed us. No, not trans people. Male people.
And then there is the fact that male people who identify as women do not actually appear to be suffering the kind of discrimination they claim to suffer in reality. They talk incessantly about "transphobia" and about how they are the most vulnerable, when the reality is in fact rather different. Every time they are allowed into women's toilets, changing rooms and rape crisis groups, their safety and their comfort is being explicitly prioritised over that of the women who would prefer them not to be there. Every time they are allowed to compete in women's sports, they are taking opportunities away from female athletes. Every time we are forced to focus the discussion on trans people being the most vulnerable and the supposed epidemic of violence against trans people, when the number of trans people murdered in the UK has been less than one per year since this information started being recorded, we become less able to focus on the very real epidemic of violence against biologically female women and girls.
In the UK and other modern western democracies at least, the factors we would typically use to classify a particular group as being oppressed and vulnerable do not seem to be there in respect of trans people, particularly male trans people who identify as women.
So when you make the point that women are an oppressed class which nobody would choose to identify into if they had any real choice in the matter, you are ignoring the fact that male people who identify as women do not actually experience the oppression that women experience simply because they call themselves women.
And if you look specifically at the impact of someone identifying as the opposite sex in all areas of public policy, from toilets to prisons to rape crisis groups to competitive sports, one thing becomes incredibly clear.
Whatever the issue is, the impact of people identifying as the opposite sex is ALWAYS beneficial for people who were born male and ALWAYS disadvantages people who were born female, regardless of how anyone identifies or what they are calling themselves.
So yes, this transgender stuff is blurring the lines of the patriarchy, but not in a good way. It is still there, we are just less able to see it, and crucially, talk about it.
Let's get real. This transgender stuff, in fact, IS the patriarchy. It's just identifying as something else.