User Protection vs. User Irresponsibility
The original question and several answers given show a gap between the understand of "protecting the user" and "avoiding user irresponsibility," so let's get that out of the way.
Protecting the user is of paramount importance within the UX process.
Avoiding user irresponsibility is impossible. Simple. Irresponsibility implies a conscious action against ones "better judgement."
A lot of little examples of this distinction could be nit-picked back and forth. A better example might actually be a very complex one... airplanes. Airplanes are designed to protect the user (i.e., the pilot) in a number of different ways, but no amount of design effort can prevent user irresponsibility on the part of the pilot (e.g., purposefully pushing the yolk full forward and hitting the plane in the ground).
Several actions in an airplane (and other systems) are purposefully made more difficult on purpose. This is to protect the user! Guarded buttons, which require the user to lift a guard before hitting a switch/button, are actions that are purposefully made more difficult so that (for example) you don't jettison all your fuel unless you really meant to.
We spend a great deal of effort to protect the user in aviation (and other fields) and to prevent them from making mistakes or errors.
User Experience is About "Easy"
No. It's about "error".
ISO 9241-2101 defines user experience as "a person's perceptions and responses that result from the use or anticipated use of a product, system or service". According to the ISO definition, user experience includes all the users' emotions, beliefs, preferences, perceptions, physical and psychological responses, behaviors and accomplishments that occur before, during and after use. The ISO also list three factors that influence user experience: system, user and the context of use. (Source: Wikipedia)
Notice that "easy" isn't in there. "Easy" is good, "easy" is an element, but it is the overall experience (the "anticipated result") that is the overall goal. Safety is a huge part of that.
The US Military has a Military Standard that focuses on Human Engineering (of which User Experience is related). MIL-STD-1472F, "Department of Defense Design Criteria Standard", discusses at length how systems should be designed to promote effective work flows and safety of the user. An excerpt of the Objective of MIL-STD-1472F reads:
Military systems, equipment and facilities shall provide work environments
which foster effective procedures, work patterns, and personnel safety and health, and which minimize factors which degrade human performance or increase error.
Emphasis added by me.
The standard also has the following requirement:
4.8 Safety. Design shall reflect applicable system and personnel safety factors, including minimizing potential human error in the operation and maintenance of the system, particularly under the conditions of alert, battle stress, or other emergency or non-routine conditions. Design of non- military-unique workplaces and equipment shall conform to OSHA standards unless military applications require more stringent limits (e.g., maximum steady-state noise in personnel-occupied areas).
When something is "easy" the chance for human error is likely reduced. But sometimes something needs to be made hard in order to achieve the user experience you are looking for. We protect the user as a result, making it more difficult for them to commit an error.
Everyday Things
The term user experience was brought to wider knowledge by Donald Norman in the mid-1990s. He never intended the term "user experience" to be applied only to the affective aspects of usage... In an interview in 2007 Norman discusses the widespread use of the term "user experience" and its imprecise meaning as a consequence thereof. (Source: Wikipedia)
Indeed, let's look at one of Donald Norman's most famous books: The Design of Everyday Things.
We could quote so many portions of this book, but I'll call out a excerpt from the "User-Centered Design" chapter. In this example (Figure 7.4) a picture of a door is presented with the unlock handle all the way at the top -- making it rather inconvenient to open. Why?
7.4 A School Door, Deliberately Made Difficult to Use. The school is for handicapped children; the school officials did not want children to be able to go in and out of the school without adult supervision. The principles of usability espoused in POET can be followed in reverse to make difficult those tasks that ought to be difficult.
Emphasis added by me.
Indeed - "difficult" is sometimes good! Difficult tasks protect the user from doing something that they should not do, unless they really mean it.
"We're just designers... It's not our job!"
User Experience is a process. This design chain is commonly called "User Centered Design". A quick visit to your favorite search engines yields many results, with slightly different flows, but here is just one example:

(different examples call out different stages and names, but all to the same end goal)
If you fancy yourself "just a designer" then great. Design, and title yourself accordingly. Don't pretend to do "user experience".
There are elements to protect the user in every stage - except arguably the "design" stage.
- Strategy: What is the product we are attempting to make? This sets everything in motion - wanting to "build a plane" guides your design process.
- Analysis: User analysis, environmental analysis, task analysis, needs analysis. They are all designed around making sure the user can effectively do their job and to reduce the potential for error. Sometimes that means making something easy, sometimes it means making something hard. **A great deal of proper research should go into this step to make sure
- Specification: Requirements are important to keep everyone on track and not decide what to do on their own; rather keeping what the research has shown us.
- Design: This takes the analysis and specification and executes on it.
- Evaluation: Does all our research and design hold up? Can the user effectively do their job, with minimal errors... meaning some tasks might be a little more difficult then others, so they aren't done accidentally.
Should I Take This Hair Dryer Into The Shower?
No, you shouldn't. So how do we design for that?
If it is possible to prevent the user from taking the hair dryer into the shower, or to prevent its operation in the shower, that is absolutely the goal of the user experience process. Other stakeholders may push back for various reasons (Engineers: really hard to do; Finance: really expensive to do) but the process should allow for that discussion to happen.
Sometimes the best we can do is just put a sticker on the hair dryer. For whatever reason the user experience process ran its course and that was decided what the best way to protect the user was. Perhaps the technology didn't exist to prevent the dryer from working in the shower; perhaps it would be too expensive to integrate (who wants a $300 hair dryer!?). But the process to prevent a very real potential for error was followed and the most appropriate solution was found.