Yes, all things being equal, bourgeois democracy is the "best possible political shell for capitalism" (Lenin, State and Revolution) - the cheapest, most overhead-free, and crucially the best for hegemonising the masses. Does it follow that workers should be indifferent to the existence of democratic institutions within capitalism? Of course not.
If there is simply no difference for the working class between different bourgeois regimes, then why did the Bolsheviks - led by Lenin - mobilise the Russian workers to defeat Kornilov's coup against Kerensky in August 1917? Yes, they mobilised on the sort of basis I outlined above, by the methods of class struggle - but nonetheless, judging that the workers were not yet able to take power, they blocked this proto-fascist military coup against Kerensky's (actually not very democratic) regime. They were not neutral! If they had been, they would not have been able to mobilise the masses in such a way as made the October Revolution possible very shortly after.
You resort repeatedly to misrepresentation. Where did I claim that a republic is fundamentally better for workers than a constitutional monarchy? I never claimed we should line up with bourgeois republicans - in fact, as is clear from what I wrote, I oppose this. Yes, the working class should demand a republic, but on the basis of its own mobilisations and as part of its wider democratic and social program. Do you think it was wrong to fight for the right to vote? By your logic, isn't this just encouraging workers to have illusions in the capitalist state? Sectarian madness!
On abortion you introduce another layer of sectarian confusion, since in fact Workers' Liberty has been at the forefront of those fighting for abortion rights as part of a broader campaign of reproductive freedoms accessible to working-class and poor women - fully funded abortion on demand, universal childcare, a rebuilt health service and welfare state - and criticising those who pose the issue in the abstract, as if abortion just being legal means that most women have real choice.
More fundamentally: yes, there are bourgeois and working-class women, but that doesn't mean that women as women are not oppressed - any more than class division means that eg racism or national oppression doesn't exist. Perhaps you think the right to vote for women was a distraction from the class struggle? Or the fight against racist laws and segregation in the United States?
My point about anti-union laws is that, logically, you should be indifferent to whether they exist or not - since the existence or freedom of unions doesn't abolish capitalism, which seems to be your one and only demand. Which begs the question of how we get from here to overthrow capitalism! Are you in favour of workers joining unions or not?
Are you in favour of voting bourgeois elections at all?