I'd agree with 1 and 2 but I think you're kind of lumping all religions and all approaches to religion together.
Most religious schools, for example, are not indoctrinating children into a cult - if that were so many more people would be C of E, but most people who go to such schools don't believe in God and aren't religious. Ditto my kids went to a Jewish school, they don't believe in God and our kids are totally free to follow Judaism as a religion or not as they get older - people often view all religion through a Christian lens (ie, that faith in God is essential) but it doesn't always work like that, or think all religious upbringings are dogmatic and coercive. They can be, it's true, and it's awful when they are, but they don't have to be.
Also they assume people have to be old enough to 'choose' a religion but Judaism, for example (and Islam, I'd imagine) involve a lot of learning about reading the language and general context, especially if you're not in Israel, so actually you do need to grow up immersed in it culturally if you are to be able to participate, but that's not the same thing as it being demanded you believe in God or being told you'll go to Hell if you misbehave. Obviously, no one should demand a child follows a religion, but being taught about your religion and culture is not 'idoctrination' in that religion any more than breaking crockery at a Greek wedding is 'indoctrinating' kids who see it into being Greek!
The French model of trying to avoid religious dress and symbols seems to have backfired and been a source of division, so it isn't something I'd recommend.