This is a provocative question to consider. At first I was thinking for instance someone calling themselves a Christian. As a term, a follower of Christ, that is very wide open as to what someone's interpretation of that means to them. It's an open-ended thing, and can be understood in many different ways.
However, in thinking about it further, let's take for example a case where you are following a very specific discipline or practice such as Tai Chi Chuan (taijiquan), which I practice and pursue in knowledge. Sometimes in watching Youtube videos I see someone performing what they call Tai Chi, and it really is what I call "Faux Chi", where it's actually not following the rules of the form at all. Even though within Taijiquan you can have variations of the form, it will all generally follow certain rules, such as keeping the shoulders down, lead with the waist not the arms, wrists a certain ways, steps a certain way, etc. And of course there are different schools or styles, such as Cheng or Yang family taijiquan.
But when someone just free forms "something" that looks Tai Chi like, it's actually not taijiquan. At best it's an "exercise" or "stretching", but it's not playing the actual form. While I may give them credit for finding the form attractive and wanting to do something like it, it's really not Tai Chi and it shouldn't be considered just as valid as the actual form that follows specific rules. "You can do Tai Chi your way, and I can do it my way," is not valid if we're not just talking about how certain postures are done differently between various schools, but rather no foundational structures at all that make Tai Chi what it is to begin with.
So to answer your question, it really depends what someone is claiming, and whether or not it's claiming to follow a specific school or tradition. If it's just all made up stuff with no understanding of the discipline at all, then that's not valid to just call it that because you want to impress people with your flowery movements.
In the above example, I would respectfully attempt to explain that what they are doing isn't actually taijiquan, while admiring their attempts, and then encourage them to explore that if it were a good fit for them. What would hopefully be accomplished by that would be their growth, learning from an ancient discipline handed down by various lineage holders to qualified students to become masters themselves and teach others.
Otherwise, I wouldn't push it, and just leave them to their illusions if it made them happy and they weren't actually interested in learning the real thing, like wanting to play the air-guitar at a party, versus knowing the actual scales of a real guitar and learning how to actually play one competently.
