There has been some significant amount of discussion at various "Irish" web pages which includes discussion of that aspect.
If I were to backtrack through my browsing history, then spend a hour or so sifting through all the rest of the discussions to provide source info as to the babies born to unwed mothers typically not being baptized by the local Roman Catholics, in the era that the Tuam "Mother and baby Home" was in operation -- then what?
Would that be significant to you?
It may matter less to our sensibilities now, but to the persons there in Ireland at the time, if one was not baptized then they were looked upon as being surely damned.
Un-baptized persons would not be typically buried in the same cemeteries as others. I did encounter the remark (amid all the reading I did on this issue from sources other than here on FR) that cemeteries in which those of the RC church were buried in, were considered "sacred cemeteries".
There was enough early childhood death -- that there were dedicated "children's" cemeteries too, with one of those some miles from Tuam alleged to be among those checked against the lists of the those who died in childhood at the Tuam facility.
There is a cemetery across the road from the facility. Have you seen it on maps? They were not buried there, with the locals seeming to "know" that persons not baptized (not just "Home Babies") would be turned away or prohibited from being buried within the same cemeteries as those who had been baptized.
In Ireland, those now digging through records have found mention of designated burial grounds at other old work houses (but no "vaults" that I have heard of) and then (still?) those same burial grounds used when some of those same properties were also used as "mother & baby homes", much in the same manner the one in Tuam was.
But so far as I know -- there has been no indication there was any sort of recognition or formal designation at Tuam for "burial" as at some other sites (old work houses and mother & baby homes) like a map indicating where people would be buried, or other mention of burial ground there -- much less any purpose built "burial vault".
There was some small mention of a few coffins once ordered for or by the Tuam nuns -- but there were nuns which passe away over the years also -- with some of those at least having been buried at the 'Grove Hospital' facility just up the road from the mother & baby home, which when the Bon Secours sold that 'Grove' property, they disinterred about a dozen or so nuns who had been buried there over the years. I guess that makes sense as the property was to be developed for something other than a hospital, and grave sites don't mix well with homes and commercial properties, so the nuns moved them to another location, on land they owned I presume. None of this is against the nuns per se, but there was mention of it in the article about the ground penetrating radar having been used at the Tuam site.
I could check again on one particularly prime source which had been posting old newspaper clippings -- in which there was some info of possibly exculpatory nature -- strongly hinting there was some underground area which may not have once been a septic tank. Or else an old sewage tank had been cleared out for another use -- some time (perhaps many years?) after it had fell into disuse -- such as yet another septic tank having been installed rather than relying upon one possibly built back in 1840. It does make some sense that those type of considerations are at least logical or reasonable possibility.
Yet still, there had to have been at least one tank on the property at some time or another. First=-- it was a work house (read -- poorhouse) then it was empty for some years before the Army used it (I forget which years exactly) before the Bon Secour nuns relocated a mother and baby home from another location.
As to the rest of your anecdotal type of comments -- those may be all well and fine, but those are from your own experience here in the States -- not Ireland between the years 1925 or so to 1961.
Even here in the States attitudes towards unwed mothers was during that same time frame as the "Home" was in operation, were frequently rather "icy" for the mother, but perhaps less so here in the U.S. as to the children -- but not always so nice for them either.
People can be cruel.
You wasted quite few words to basically say that you have absolutely no proof that the babies were not baptized. Just speculation that attempts to paint the Catholic Church in a negative light.