Not analogous in any meaningful way.

Let's try it. I'm thinking of a group of people. This group of people is disproportionately subjected to police violence, including police shootings. This group is more likely to be prosecuted when accused of a crime, is more likely to be convicted when prosecuted, and gets harsher sentences when convicted. What group am I describing? Hint: The answer is that all that applies to both black folks and men, and usually to similar degrees (close enough that some measures have a wider sex gap and others have a wider race gap). And that's not even a complete list of similarities.

By the vast majority of measures the way men are treated by the criminal justice system compared to women and the way black folks are treated by the criminal justice system compared to white folks line up (other non-white racial groupings tend to end up somewhere between). Race and sex also both apply, meaning that black men get treated the worst and white women get treated with kid gloves. Depending on the specific measure, sometimes the gender gap is actually wider than the racial gap but that again depends on the specific measure (for example black folks are more disproportionately killed by police than men are but mostly because that would require more than 100% of police shootings to be men instead of merely 95%, while men get disproportionately harsher sentencing for many crimes than women to a larger degree than black folks do compared to white folks).

I personally know a white woman from here who got busted for drugs in another state, was released on her own recognizance pending her hearing, fled back here, was eventually picked up, spent a few days in jail while the other state decided it wanted to extradite her and made arrangements to transfer her, went before a different judge and was released on her own recognizance pending her new hearing date a second time, despite demonstrably proving she was a flight risk. That's doesn't happen unless you are a white woman, preferably a young, pretty one because those traits both carry further privileged treatment by criminal justice.

Unless you want to argue that men are underprivileged in society.

I'd argue you are operating from a bad model. The core problem is that a lot of social justice models are ultimately built upon a bedrock of Marxist class conflict, with people being assigned into roles of bourgeois-analog "oppressor" and proletariat-analog "oppressed". The problem is that the degree to which Marxist class conflict actually works as the basis for a model is basically the degree that whatever feature you are basing it on functions as a proxy for economic class. For race, it does well enough in the aggregate that it works, albeit imperfectly. For sex, however it's a poor fit.

The trick is that to justify fitting sex into a model based on class conflict you lie to yourselves by looking at the sex distribution at the very top and pretending that that tells you anything useful about men as a whole (this is a fallacy of composition). Or to put it another way, Nancy Pelosi and ~~turtle lich~~ Mitch McConnell have more in common with each other than either of them does with men or women as a general class.

A consequence of this is a whole series of apologetics and the like to try to justify why the model still holds even when evidence seems to run counter to it. Like using epicycles and deferents to try to make a geocentric model of the solar system fit reality. Except it;s all things about how "the patriarchy hurts men too" in exactly the way you wouldn't say "capitalism hurts billionaires too" and that kind of thing. Like why in a system allegedly built on male supremacy would men be treated worse by criminal justice than women, in all the same ways that this same system that is also allegedly built on white supremacy treats black folks worse than white folks? The short answer is that it's unfalsifiable, the model can be stretched to fit any measurement of reality.

A better though still imperfect approach is the concept of malagency which seems to do a better job of actually predicting how western culture actually treats people with respect to sex. The core notion of malagency is that society treats men as hyperagentic (that is men are perceived to have greater agency/responsibility than they actually might) and women as hypoagentic (that is women are perceived to have less agency/responsibility than they actually might). Applied to criminal justice, this directly explains things like men being given higher bail and longer sentences for the same crimes - men are seen as more responsible for their crimes, and so "deserve" a longer sentence. Even when a man and woman do a crime together, the man is often subject to higher bail or a longer sentence, which makes no sense as "privilege" but makes all kinds of sense if men are treated as having greater agency. When having lots of agency/responsibility for your actions is beneficial, this leads to better treatment for men and conversely when having greater agency/responsibility for your actions is not beneficial, this leads to worse treatment for men.

So for example, imagine we both saw a news headline on Reddit or Lemmy about a young woman throwing her newborn baby out a window, leading to it dying in the ambulance. Presumably under a model of privilege and male supremacy, we'd expect lots of blame directed at her and her behavior because she's a woman and any comments questioning her guilt or supporting her to be downvoted. Under malagency, you'd expect people to immediately start looking for ways to diminish her responsibility for throwing her child out a window and maybe even poking at the possibility of the father being at least partly to blame in some fashion for the baby killing and downvoting anyone laying responsibility for the killing squarely on her, because the slant is minimizing her agency for what she did and if possible assigning agency to a man.

What do you think we'd actually see in those comments? Hint: this isn't a hypothetical, it's a recent news story that's popped up on Reddit and you should take a look. It...strongly resembles what you'd expect under malagency.