Yes, though for some, all of these are equally menacing. A horrible rash is just that, regardless of the degree of latex that caused it. I didn't bother to type that to parrot something I've read or whatever, but because I've experienced horrible rashes personally from these plants except the Euphorbia and Plumeria because I knew ahead of time (and haven't had poppies since 'becoming' allergic.) I went through hell trying to figure it out and was just trying to prevent anyone else who reads this from the same suffering. Yes, there's plenty of info out there if you realize some of your 'old friends' are suspects.
I used to NOT be sensitive/allergic to Ipomoeas (morning glories, sweet potato vines, moonflower vine,) fig trees, and Asclepias FOR SURE. My daughter and I had monarch caterpillars hatching in the house, and I picked leaves for them daily, and handled broken parts of several Asclepias species regularly. When I was a kid, I thought the sap was the interesting part, break off the stalk and watch it ooze out, I definitely touched it and definitely didn't go wash hand after. Same thing with dandelions that drip white stuff.
I've been picking figs for years, and using the leaves to make a tea for fertilizer but am suddenly not able to touch the sap at all w/o getting a rash. I've had various Ipomoeas for decades, which I would propagate constantly all summer, DEFINITELY getting sap on myself with no ill effects. Now it gives me a rash. Last summer a neighbor came by and asked if I could pick some figs for him because he was newly allergic to the sap also.
So, yes, I would say you were lucky. Something that was completely harmless to your particular skin yesterday may not be tomorrow. Sensitivity to urishiol can also be transient and variable for a single person throughout a lifetime, and latex sensitivity is equally as unreliable.
I will continue to share this info in hopes that it saves anyone else the extended misery I experienced trying to figure this out, operating under the same false assumption that any plant that was harmless before should/would definitely still be. Spending 2 summers with 'constant mystery poison ivy' is really uncool and unpleasant, and you can still see where some really bad spots were, some 2 years ago now.
Though less of an irritant these other plants may be, I wouldn't attempt to 'rank' the experiences (going to ER for sap in eyes vs. excruciatingly itchy, oozing dermatitis that lasts for about 2 weeks and occupies every waking moment with misery and prevents sleep) since thankfully I haven't experienced the former, but simply hope folks could avoid any of this via prior knowledge.
I have Ipomoeas, Euphorbias (including about a dozen pencil cacti scattered around different pots,) Plumeria. There's no reason not to have these plants, not saying that at all. Just that touching the sap could have consequences, which I or anyone can avoid by not touching it.
If a search happens to bring this up for anyone else investigating a mystery rash, consider any Aroids or Commelina family members in your collection. Philodendron, Tradescantia, Callisia.