Terence Copley's Indoctrination, Education and God makes a good case from the moderate Christian perspective that complaints about "indoctrination" by people wanting to keep education secular miss the mark because all school systems indoctrinate to some degree and for some purpose: it's a matter of what doctrine is to be promulgated, which makes things difficult in any society with more than one (non) religious and (non) spiritual viewpoint; even leaving religion out altogether and saying it's "the job of home and church/ place of worship" is powerfully indoctrinating children with a hidden curriculum of marginalization of faith in daily life- not to mention that matters germane to faith-based worldviews are discussed overtly across the secular curriculum in a way which must be "balanced" somehow.
For excluding faith from state education to be fair to those with a Biblical worldview or other paradigms one would need to at least cut massive holes in the so-called "social and emotional aspects of learning" programs, or abolish them altogether in a Bonfire of the Vacuities; one reason for my children being privately educated in a Christian setting is due to friends warning of a couple of (militant?) teachers at the local comp who have stretched SEAL to force children to waste two hours of their week allegedly in "enrichment of... intra- and inter-personal intelligences" through practices which encourage unlimited self-disclosure trampling upon their privacy and ours, promote New Age "relaxation techniques" and forms of "stress relief" with anti-Christian Eastern religious influences to ostensibly get kids through exams, and introduce sessions on "emotional literacy" where significant moral issues are discussed but pupils are told there is NO right or wrong answer !
Many mothers trust blindly that a school described as a "community" primary or comprehensive will be neutral on value-laden issues, not necessarily reinforcing what is taught at home but at least respecting it- then I realised what some teachers think they can get away with! And all too often when parents do complain they seem to believe they have a right to expose your dcs to anything just because they are professionals ...well none of THAT arrogance at the school dh and I chose 
. Shame that we have to pay for it in addition to paying the same tax money as state system users, and that good Christian (or Jewish, Muslim, Hindu, etc.) schools are few and far between.
The fairest thing to do IMO would be vouchers for private schools and more free schools approved (and non-Christian ones too; it is being suggested that Gove's team are employing discrimination in approval of proposed Muslim and Hindu free schools/ academies which are badly needed in our inner cities. After his efforts to downplay people of colour in History lessons I fear the DoE may be biased against British Asian community, which would explain above.) Those remaining in the state system would then have more competition and parents more choices so they would have to be honest about their own "indoctrination", however it was structured. As you will never find one philosophy of life which all British parents agree on their children being taught I cannot see any other way being fairer to people overall across religion/belief, socio-economic and ethnic categories. Trying to create a "neutral" common school system just leads to a few powerful groups setting the rules for everyone.