Secondary school appeal - was admission policy applied wrong?

You should have had some kind of information after the first allocation of places which stated which category you were considered as when they were allocating places. If it says you were in a faith category then nothing that you can do. If it says you were in a distance category or something similar then you need to track back and check what information was required to prove your faith category. You mention a birth certificate but was this just attached to the LA application or what. In most faith schools the onus is on the parent to get the extra information to the school as it is the school that check your faith credentials. If it was sent to the LA then they normally do not pass them on to the school as they would claim that the process of giving to the school was clear and was for the parent to arrange.
If you submitted the faith documentation correctly in the required time frame and they have not classed you as faith category then you might have a case that a mistake has been made but the panel will need categoric proof of the school / LA making a mistake which can only come from going to the appeal.

For our faith place I had to tick faith in the main application. I then reiterated on the SIF and had to explain which category I was under and provide dates supporting my church attendance and other activities along with those of dc that made us eligible as well as a form for the Vicar to complete stating how long and on what basis we had been involved at Church.

You need to look at the original application, not the supplemental form, to check that at that stage you did say you were applying for a fair place. It sounds like they think you ticked community place here.

Being baptised and attending was not enough, I had to state the extra voluntary work DC and I had undertaken for at least 3 years to be eligible, is there a chance your school has similar?

Or have you only submitted it after the first allocations were made?

I think what lantharnum is asking is which box was ticked on the original application form (not the SIF)

If that was submitted correctly, then they are on the face of it wrong in asserting that you applied for a community place.

Would your DS have been offered a place had he correctly been categorized as a faith applicant? What faith categories were there, which do you think DS would have been correctly placed in, and did all applicants in that category receive offers? Being baptised may not be enough if there was an attendance requirement, or if certain denominations are prioritised ahead of others.

What happens to unsuccessful faith applicants? Are they then treated as community applicants?

What did the LA placement letter say your dc were categorised as for admissions purposes and how were places allocated? Did they acknowledge receipt of your supplementary form?

Beyond baptism certificate were there any other faith based qualifying conditions - e.g confirmed attendance at church and did you supply those?

It sounds like either you ticked the wrong box, or your application got wrongly categorised after receipt. Do you have a copy of your original application showing clearly that you applied on a faith basis? (Attaching the baptism certificate wouldn't be relevant if you ticked the wrong box, or if the faith qualification is based on something other than baptism.)

Your DC's primary school might be able to advise; they're likely to know what's what for the local secondaries.