"As a step-parent you have to treat them just like your own child, otherwise you may as well not bother and forget the whole thing."
Treat them as well as your own child yes, but interfere in attitudes (politcs/religon/morality) that their parents wish to inculcate? Definitely not! This is especially true when the biological parents are alive and you are not acting 'in loco parnetis' but rather as a 'good friend' to the child, the boundaries should be respected and tongues bitten however difficult this may be at times.
You are looking at it only from a step parents view point and not seeing it from the viewpoint of the biological parent.
Try imagining how you would feel if a step parent to YOUR biological child was going against something political/religious/moral viewpoint you felt strongly about. Get away from immigration, it could be anything, attitudes to female equality, attitudes to drink, drugs, religion.
Step parents should mind their own business and leave these politically charged questions to the biological parents! Anything else is only going to cause family discord.
An eleven year old is too young to 'make her own mind up' and is inevitably heavilly influenced by others, and on the subject in question there is no such position as 'impartiality' (the OP clearly has strong views herself or she wouldnt have such a strong desire to influence her SD). Why is she even raising this here rather than with the girls father anyway? If he shares the OPs views on this matter then he, not her, should take the decision if he wants to deal with it by putting an alternative view to his daughter. If he doesnt then she should butt out too.