In the June 1840 General Registry Office index of births there is listed a Henry Woodfield. That is incorrect - he should be named as Henry Masters. I have a copy of this Birth Certificate. Henry was born 13 March 1840 in Warwick, England. The "Name and surname of father" is James Woodfield - his occupation is Boatman (Because this is a documentary statement of paternity I guess that James was present in the Registrar's Office when the birth was registered). The "name, surname and maiden name of mother" is Ann Masters (i.e. only two responses for the three required pieces of information). The informant is illiterate and therefore it is the profession hand of Mr Margetts the Registrar that writes the words within the entry "The mark X of Ann Masters, mother, Inmate at George Masters' Laborer Saltisford St Mary". The birth was registered after the Christening - the birth was registered on 7 May 1840. The Christening correctly names the child as Henry Masters.
Although they were a little slow in getting the baptism, and a little slow in registering the birth, they were even slower in marrying. Henry Woodfield and Ann Masters married on 27 March 1843. James is a Laborer (it could be read as Labour).
On a birth registration a child did not have a surname only a first and sometimes middle name. If the registration indicates that the parents are a married couple then the birth is indexed under the fathers surname, if the registration indicates that the couple are not married then the birth is indexed under both surnames. If no father is on the registration then the birth is indexed under the mothers surname.
In the case of Henry, if the mother was only shown as Ann Masters ie only 2 of the required responses you refer to, then that indicates that the parents were not married and the birth should have been indexed under both surnames. If the parents had been married then the 3 responses would have been Ann Woodfield (nee Masters). It does appear that the GRO have erred in not indexing the birth under Masters as well as Woodfield.
It would certainly be not uncommon for a child to be baptised before registered as you had, I believe, 6 weeks to register a birth and many children were baptised shortly after birth.
To echo what
KGarrad posted, I think you are being a bit unfair, Registrars only wrote down information they were given, and it was not always accurate, I'm also not sure where you get the idea that mothers were an afterthought.
Andy