Pornography Addiction
It is certainly true that there are various right-wing and/or Christian groups do claim pornography addiction as a reason to revoke basic human rights, further marginalize sex workers, and justify violence against sex workers... that doesn't mean they invented it.
It's worth examining how this is working with pornography and the ways it ties in with the various fashy parties determined to rule the world we all live in.
Actual Pornography Addiction
Actual pornography addiction has its roots in similar addictions such as gambling - it is a situation where the individual becomes obsessed with it as a source of positive feelings, to the detriment of themselves and those around them.
Symptoms of it include a full blown obsession, a loss of interest in other enjoyable activities, spending money needed for essentials on the focus of the addiction, engaging it under risk circumstances (such as while at a job that you really need to keep), suffering anxiety and frustration when unable to indulge, etc.
Importantly, with these kinds of addictions, they are often not really about what what they appear to be. People get addicted sometimes because it's a reliable source of dopamine hits, or because it provides an escape from harsh realities around them, etc. Taking the focus of the addiction away does not fix the underlying cause, and often leads to them finding a substitute addiction.
How much it applies to any given member of that community is impossible to say, as the whole group is irony poisoned and also obsessed with performative behaviour.
And as a side note, if someone dear to you has similar behavior, whether its in relation to porn, sex, gambling, video games, or anything else - then it is generally considered the compassionte thing to try to get them to realize it and work towards addressing both the addiction and any underlying causes in their life.
Right-wing "Pornography Addiction"
When people who have nothing but contempt for psychology and sex therapists say "porn addiction" or "sex addiction" they are villifying sex workers and objectified persons, blaming them for the violence done against them and completely unrelated ills in society.
They consider it "addiction" if you develop a crush on someone other than your spouse, have normal sexual fantasies, occasionally want to enjoy pornography, are curious about visiting a strip bar or even just masturbate... under any circumstances.
They are closer to anti-pornography than concerned for addiction, and has a long, long history. I would hope BABD followers would be aware we are definitely not anti-porn and we actively support sex workers.
Obviously, the real goal is to give them more control and more avenues to suppress people. This is clearly illustrated in the ways Project 2025 both wants to outlaw pornography and define "transgender ideology" as pornograpy. You can see between the lines, the goal isn't to make people better, the goal is to criminalize the existence of people they look down on.
The harm of co-opting
At face value, it's easy to see why the proposed solution to this is just to say it's not real, it's right-wing nonsense, etc.
But that creates two problems. First it means there's people with a problem that is being denied, and secondly it kind of ignores the real overall goals by missing the forest for the trees.
People whose lives are harmed by behavioural addiction need a framework to be able to address it, and need other people to take it seriously and not just dismiss it as "made up". This applies to gambling, shopping, gaming and pornography.
Think about it, when was the last time you saw a swastika on display as a symbol of positivity? Think "incel" is ever coming back to the LGBTQ people who struggle to find people accepting of them?
Secondly, the reactionaries co-opting it are not "making up" a boogieman. They're not that imaginative and they're much, much more dishonest and malicious.
They're actively spreading misinformation in an attempt to gain for authoritarian power to use to harm people. They're actively trying to undermine the work people have done to help people, stripping the actual research away and placing themselves as the authority on a topic of public wellbeing that they see only as a cudgel.
Because they won't stop at just claiming to be the experts on pornography addiction, they'll claim to be the experts on gambling, drugs, alcohol, gaming, shopping, etc. All their advice will be what's convenient for them, and their friends.
Same way all kinds of psychological concepts get co-opted into torturing people under the claim of conversion therapy (which does not and has never worked, in any capacity), often in the name of profit as well as oppression.
So my recommendation is be less concerned about the term appearing, and more concerned about whether it is in the context of warning people their obsession is harmful - or just trying to trick people into agreeing to authoritarian control.