Alabama Republicans pass most restrictive abortion laws in US - no exceptions for rape または incest 

That doesn't seem fair for the victims of rape and incest at all.

Yeah it's rubbish. Just imagine going through the extremely traumatising experience of rape itself AND THEN along with all that trauma, unwillingly having the next 9 months of your life made even more hellish and a constant reminder of the very experience you're trying to recover from.

Doesn't contain an exception for underage victims of rape either. Apparently Republicans aspire to be link, which forced an 11 year old girl to carry the pregnancy to term and give birth after she was raped by a family member.

Also doesn't seem to contain an exception for fatal foetal abnormalities like link, where the brain is missing. The majority do not survive birth, and among those that do, almost all do not survive for longer than a few hours or a few days at most (and have no capacity for thought, consciousness or even pain) . So instead of having the choice to terminate the pregnancy, Alabama women will be forced to go through the traumatic and painful experience of giving birth to a stillborn infant, or having them die soon after.

Edit: Of course, there's also the women who will feel they must try and get a back-alley abortion, even at considerable risk to their life and health.

Is it possible to change that law by petition? I mean, I know signing petitions wouldn't do much these days so would there be other ways to change that law?

^Unfortunately don't think petitions will do much. This is a 'tyranny of the minority' sort of situation and they don't give two shits what other people want. Probably the only way it's gonna change is if:

A. Republicans are voted out at the next state election
B. The law goes to a challenge at the US Supreme Court, which is what all these recent restrictive laws have been leading up to. They will either be found unconstitutional because of Roe v Wade (which found that the Fourteenth Amendment protects a pregnant woman's liberty to choose whether or not to have an abortion), or the Roe v Wade decision will be overturned and the law will stand. All these anti-choice laws are being passed now because as of the Trump presidency, the Supreme Court has been stacked with conservatives and the overturning of Roe v Wade is a real possibility.

One of these reasons I urged people to vote against Trump btw. It was the crucial time to ensure the Supreme Court isn't biased towards one side of politics.... and now it is, and will be for decades. Judges have lifetime tenure - they can stay on until they die.