Circuмcision is utterly unnecessary at its absolute best, but the circuмcision performed by medical professionals is not that of the Old Covenant. 

Indeed, the modern version is truly vicious a very expanded version of what was. God never requested circuмcision like they do today.  But without the ritual background, the history, there is no circuмcision at all.  Its roots are religious only.  Just because they call it a "medical procedure" doesn't mean it is a "medical" procedure.  Circuмcision has no medical purpose whatsoever.  For that reason, intent behind its resurrection (sic) becomes obvious. Circuмcision is a ritualistic, religious practice foisted on us more barbaric than imaginable, and as such, it is an emblem of the power and intent of the Occult Jєωs. Why else would huge percentages of baby boys be circuмcised if it wasn't religious?

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Of course it has religious roots, no argument there.  But at a certain point, the intent behind some action along with the accompanying rituals (or lacktherof) attached to the action make it no longer religious, or at least certainly on a predictable basis make it so emptied of religious content that it is not religious. 
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There are loads and loads of things today that had an initial religious "root" in some way or another that are quite obviously, as usually used, not religious.  Fish fries on Friday in 2017 have virtually nothing at all to do with businesses catering to Catholics who were following Church law; most Catholics today who eat fish on a Friday don't even know they're supposed to be abstaining from meat, so how on earth can we say that if they go to a fish fry they're observing a religious law?  Unleavened bread has its origin at the passover, but you can make unleavened bread without celebrating a Jєωιѕн feast.  So on and so forth.  The Old Covenant rite of circuмcision was a religious ceremony that involved the removal of a small amount of the male child's foreskin.  If you remove the religious ceremony from the event, you're not left with a religious ceremony.  Even if medical circuмcision was the same materially as the Old Covenant form of circuмcision (which it isn't, but supposing it was), medical circuмcision would still be a medical procedure, not a religious ceremony.
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I find it somewhat difficult to buy the idea that Occult Jєωs are behind the medical push for circuмcision, for two main reasons.  First, they don't want the goy, so why on earth would they orchestrate efforts to incorporate him into the Jєωιѕн community?  And secondly, the trend of circuмcision is dying and was, so far as I can tell, relatively short-lived.  Can we name a Jєωιѕн conspiracy that the Jєωs have abandoned as they've apparently abandoned the circuмcision conspiracy (as evidenced by its significant drop in popularity and the virtual wholesale admittance of the medical community that it provides no health advantages)? 
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It's highly objectionable and we agree on that-- and it's definitely something about which the word needs to be spread.  Parents should not be (medically) circuмcising their boys; if anything, the procedure physically disadvantages them and wounds their generative faculties.  I would agree that it is a form of mutilation, and a very sad one at that given the helplessness of the child. I am disagreeing simply with some of the reasons you are putting forth. 

What does your Traditional Priest say on this ?

I haven't asked.  I attend a resistance friendly, independent parish and have only recently engaged the priests about various subjects.  Just not this one.  With the Council of Florence weighing in, the subject is not open to a contrary opinion.  I'm hopeful once I've talked to the priests, they'll carry this message along to Catholics because it affects so many people.  

I am distinguishing because the two are distinct.  
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Florence doesn't anathematize what we're talking about, it's anathematizing the religious observance of circuмcision by Catholics.  Medical circuмcision, so far as I'm aware, wasn't even a thing then.  There was circuмcision full stop: as religious Jєωιѕн observance.  Some parent in 1988 who trusts their doctor that circuмcision is a good thing and lets an Episcopalian nurse circuмcise their boy in the nursery isn't the object of the warning.  If they've sinned in having their child circuмcised (notice I say if because I don't think it follows necessarily that they have) then it's along the lines of negligence, i.e., of making a decision that is detrimental to the child due to not having sufficiently investigated the decision.  But even that charge is difficult to stick carte blanche because appealing to a medical professional as a legitimate authority is not unreasonable.  We might point out that the medical profession has become corrupt, and we would be right in saying that caution is necessary, but we should hesitate to fault people who trust authority, particularly at a time when information was not disseminated as easily as it is in the Internet age.  Fundamentally, that (reliance on authority) is a good intuition and one for which Catholics have not traditionally been rebuked.  If one already knows better then of course it's a different matter, but if one simply places their trust in a professional because they realize their own limitations in assessing some situation or another, blame is difficult to assign.
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Now, I've given you two reasons for the distinction between these two types of circuмcision.  First, in the one instance you have a religious ceremony, and in the other instance you don't.  That alone should render the distinction clear in anyone's mind.  It isn't a question about which is "better" or which is "worse," rather it's simply a question of whether or not they're the same thing.  If they're the same thing, then everything about the one can necessarily be said about the other.  If they're not the same thing, than whatever can be said about one is not necessarily true about the other.  
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The second reason is that the effect is similar but still very different.  The physical effect of religious circuмcision is marginal; there is some loss of blood and skin, but nothing about the male genitalia is so disturbed as to render its function any more or less capable.  This is not true of medical circuмcision, as the removal of the entire foreskin actually renders the genitalia not as facilitative of the generative act.  So there's another substantial difference between the two.
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What you're seeing are two remotely similar effects and then conflating those effects to establish a shared identity between the two acts.  But the effect of the two circuмcisions is actually quite different, about as different from piercing your ear and cutting it off.  You'll be able to hear either way, supposing that the cutting off of the ear leaves intact the hearing faculties (you don't hear through the actual cartilage, skin, and bone), but each act produces a nevertheless very different result to the body, and likewise is facilitated in a very different way, just as these two types of circuмcision are.  It's like you're just seeing two people touching their ears with sharp things and concluding on that fact that they are performing the same act, despite the one is poking a tiny needle through a small part of the ear lobe for the purposes of ornamentation and the other is using a Bowie knife to carve away the entire ear presumably owing to insanity.

Mithrandylan has given the Catholic viewpoint on this issue.

Happenby's "dogmatic" stance on it is a private interpretation of Tradition (in this case, the Council of Florence). And her private interpretation of Tradition is no better or more accurate than your average Protestant's ham-fisted attempts to privately interpret Scripture. Both are wrong.

We must follow the teaching of the Church.

Everything Mithrandylan said is correct. He seems to have all the nuances of the argument covered, so I needn't repeat him or elaborate.

Mithrandylan made a good point though -- there is no way medical circuмcision is a Freemasonic/Jєωιѕн conspiracy. If it were, they wouldn't have dropped it! Because just like breastfeeding, mothers co-sleeping with babies, and eating healthy food has made a comeback, so has "anti-circuмcision" of late. And the Jєωs consider themselves the only real humans (i.e., the only rational creatures with an immortal soul, created in God's image). They consider non-Jєωs to be goyim, which literally means cattle. Why would they want their cattle to resemble themselves and share in their dignity? They wouldn't.