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That's a tremendous waste of time and effort when 90% of the time even AFTER all that effort you won't be able to come up with a solid answer.  There's NO RISK OF SACRILEGE and it's perfectly sufficient to know that there's a mindeset and tendency very common in the Conciliar Church to play free and loose with the Sacramental Rites and to "ad lib" stuff.

You make it sound as if it takes months or years of investigation, when in reality, these days if it takes 3 or 4 hours would be a long time.

Thanks, you have come the closest to answering my original question - though you didn't fully answer it either.

You seem to think the above guide is "decent", I see that it was lifted from a guide printed by the Franciscan Press in 1995 - I immediately think the 1983 "new-code of Canon Law". Personally, I would only use it for Firestarter. Vatican II stopped doing many conditional Baptisms due to the new ecuмenical spirit. The list you sent, states validity is presumed when one is coming from those sects - so ecuмenical of them! This way of dealing with converts is false. Prior to VII, the Church took baptism most seriously and anyone coming from a false sect would need to have the validity of their baptism confirmed beyond even reasonable doubt i.e. morally certain.

I think the list is just based on a high-level view of whether those groups tend to use a valid form and have a theological view of the nature of the Sacrament that doesn't invalidate.  It does not speak to whether any of those groups tend to have a loosey-goosey, non-formal, approach to their rites, where any "minister" can just do whatever he wants.  And that's actually most of them.

To have a strict ritual to which all the ministers (aka priests) must adhere (or are supposed to adhere) and where there's no mentality where it's OK to make up whatever you want ... that mentality tends to be limited to the Eastern Orthodox (and for our purposes, since the question is about Novus Ordo, the Eastern Catholics).

Such rigorous adherence to a fixed ritual is VERY MUCH CONTRARY to the Prot mentality, and there's widespread adaptation ... and actually it's precisely what you're referring to in the Novus Ordo, where that attitude has become very prevalent among them as well.

So, IMO, unless someone's coming over from Eastern Orthodox, or an Eastern Catholic Rite ... I would say a conditional Baptism is warranted and even advised.  I heard once from some older priests that in fact it was common practice that if you came from some Prot denomination, they would conditionally baptize you as a matter of course (for this reason).  There was never this attitude (that seems to be prevalent among the Traditional clergy) where they felt they must to a case-by-case investigation ... almost like one a marriage tribunal would do when researching an annulment.

What's being condemned by Trent is the scenario where someone wants to become Catholic and you just baptize them without making any inquiry, where they might tell you that they were baptized Eastern Orthodox or something obviously valid, or perhaps even Catholic when they were infants, but then at some point they left the Church, etc.

Depending on which denomination you came over from, one could make a general judgment (oh, Baptist? ... let's conditionally baptize you.  oh, one of the strict Lutheran groups? ... not needed, etc.).  It suffices to make a judgment based on a generalization based on group without a case-by-case in-depth investigation.  Nobody has the time for that, and in 90% of the cases you won't get sufficient information to make a judgment anyway.

There are extremes on both sides, with a willy-nilly conditionally baptize anyone who comes to you with no questions asked even if they just have negative doubt on the one side, and sinful unless you can positively establish positive doubt in each specific case on the other side.

As long as you're making prudent judgment based on asking questions, that suffices to not cause injury to the Sacrament, and there's no risk of actual sacrilege due to it being conditional.  What Trent was trying to avoid was guys going around baptizing everyone (including those baptized Catholic) "just in case", say, the priest did it wrong (negative doubt).

What is the case with Matrimony?

So, that's more a question of the priest's jurisdiction to witness.  In the Roman Rite, matrimony is confected by the couple themselves, and the priests serves as the witness.  Canon Law requires that those baptized Catholic confect matrimony before a witness who has the appropriate jurisdiction ... or else it's invalid (you just have to be baptized Catholic, so that even if starting the day after your Baptism you were raised a Protestant, you're still bound by this ... a not-entirely-uncommon ground for annulment).  Now, at one point we looked at the details here, but there are some exceptions, such as if you cannot find a Catholic priest with the necessary jurisdiction in a certain timeframe, then you could just have any priest witness, and if no priest then some lay people, etc., though don't quote me on the details since I can't quite recall.  In theory, the Church could designate a non-priest to have the jurisdiction to witness marriages, since the Power of Orders isn't required to basically just act as a witness on behalf of the Church.  So, as we know the neo-SSPX have agreed to get all their marriages witnessed by Novus Ordo presbyters sent by the NO "bishop".

So, if you're a Traditional Catholic outside of neo-SSPX, you have to make a judgment that the Church supplies, since we don't have priests with the jurisdiction, or that the Canon Law applies where we can't have access to a priest with jurisdiction (since they're all in the Novus Ordo, depending on your theological perspective, or else none exist at this time, except perhaps in some Eastern Rites).

Where doubtful Orders might come into play would depend on the details of Canon Law I can't quite remember now where it says you can go to some other priest if one with jurisdiction isn't available in a reasonable amount of time (and whether the language requires that it be a priest) ... or whether you simply rely on God supplying due to the Crisis.  If I have some time, I'll see if I can dig up the Canon Law.

Now, in the Eastern Rite, the priest is actually the minister of the Sacrament and confects the Sacrament, so that's a different ballgame and I'm pretty sure (though not 100% certain) that you would need a valid priest over there ... but then most Eastern Rites still have valid priests.