There are many thing in sharia law that modern people (olny disbelievers) find outdated. So can we update sharia law.
That a woman can't have equal inherentense And why can't a woman live alone and why can she go outside alone.
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No you can not update Shariah law, especially something which is proven through revelation, as it has been forbidden and severely condemned.
وأن احكم بينهم بما أنزل الله ولا تتبع أهواءهم
And judge between them by what Allah has revealed and do not follow their inclinations
ومن لم يحكم بما أنزل الله فأولئك هم الكافرون
And whoever does not judge by what Allah has revealed - then it is those who are the disbelievers.