I hope you don't mind, but I updated your copypasta too, with a few changes:
I updated the sources to be inline, so I had to change the wording for a few. I made the sources into a list and added another one: a RAINN article about stats on the offenders. I removed all mentions of "I", which seemed weird if other people were copypasting it. I removed the swearing, so people won't find it easy to reject out of hand (and switched "bitch" to "b***h" when quoting). I removed the "more than the number of Jewish people" which is true for Jewish Americans (there are 14-18 million worldwide) and felt it weird to specify too much.
The rates of false rape accusations are the same as false accusations for any other crime - between 5-8% depending on the study. As with all false accusations, there are sentencing provisions in place for the crimes of false police reporting, obstruction of justice, interfering with a police investigation, perjury, etc, at the discretion of the judge. "She should get the same amount of time as the guy she accused!" is, frankly, absurd, because rape and lying are not equivalent crimes.
That 5-8% is the percentage of reported rapes that are proven to be false or for which not enough evidence could be gathered to build a court-worthy case. Depending on the laws where you live, "legitimate rape" could be dismissed if the perpetrator didn't use violence, if the victim was too intoxicated to give an accurate account, if too much time had passed to collect viable evidence, etc. Just because a rape accusation is made and then dismissed doesn't necessarily mean the accusation was false, just that no one could prove it in a court of law.
Rape only has about a 40% reportage rate and over 95% of those accused will never spend any time in jail. There has to be some truly horrible planetary alignment to get someone falsely accused of rape imprisoned.
One of the reasons so many rapes go unreported is because of shit like these threads that automatically assume the accuser is some "lying b***h" out for vengeance or covering up "regrettable sex" or whatever (and claiming that false accusations are the REAL problem, when it's so, so much rarer than actual rape). No one wants to go to the police or even tell their friends if they're afraid no one will believe them. When you make a big deal about false accusations, or when you try to pass harsh punishments for those who make accusations that can't be proven (see second bullet), you make victims afraid to come forward. False rape allegations hurt future victims, too. Every time one makes a headline, it makes it that much harder for future victims to be believed because the false allegations stand out in the popular consciousness.
Rape tends to happen between two people behind closed doors, with someone the victim knows. Don't presume to understand "what really happened" when your buddy says he was falsely accused or whatever. Look at the percentages and ask yourself if your buddy is really such a special snowflake or if there's actually a wee little chance the accuser is telling the truth.
Studies of men on college campuses have revealed that roughly 1 in 25 men will admit to behaviors that would be legally classified as rape - but they won't admit it if the word "rape" is actually used. They'll say, "Yeah, I used violence or the threat of violence to get a woman to have sex with me," and out of the other side of their mouths will say, "But I'm not a rapist." If someone you know denies being a rapist, that might just mean they don't consider what they did to be rape when legally and morally it is.
About that 1 in 25 - in the US, that's 6 million men. That's more than the number of single mothers, or postal workers, or grocery clerks. How many of those demographics do you interact with on a daily basis? Because you've probably met more rapists. Think of how many men you know, and then realize that 1 in 25 of them is a rapist. There were probably 6-8 rapists in my high school class. How many were in yours? How many are in your frat or your classroom right now?
Think of how many women you know, and realize that 1 in 6 has been or will be raped in her lifetime (a conservative estimate; some researchers place that number as high as 1 in 3). 1 in 6 women will be raped, but only 1 in 25 men will rape. Those rapists in your classroom have probably done it more than once, and will continue to as long as you dismiss their behavior as "that b***h made it up."
3% of American men (1 in 33) have experienced attempted or completed rape in their lifetimes (comprising about 10% of all rape victims), and 21% will experience sexual violence other than rape. In cases of rape with a male victim, only 6.5% of perpetrators are female. So as a man, you're more likely to be raped or sexually abused by another man than you are to be falsely accused of rape.
Sources:
RAINN - The Victims - Information on who sexual assault victims are.
RAINN - The Offenders - Information on who the offenders are. 73% are non-strangers.
The Hathor Legacy - Rape statistics - Lots of good statistics, tons of sources at the bottom (but all books, sorry)
Debunking "One in 4 or 5 men are rapists" statistic - About the deliberate misreading of stats.
Newsweek - When Campus Rapists Don’t Think They’re Rapists - This more about men who will/want to rape but won't call it that.
Al Jazeera - Serial rapists commit 9 of 10 campus sexual assaults, research finds - Includes quotes from Lisak study.
How Many Men are Rapists? - Cites Koss study(Paywall), which is where the "1 in 25" is from.
David Lasik - Repeat Rape and Multiple Offending Among Undetected Rapists
Koss study found 4.5% while Lisak found 6.4%. Both of these were studies of men on college campuses, so the general population might actually be higher or lower, but this is the best estimate anyone's got so far.
A UN study indicating that worldwide, the number of rapists in the population averages 1 in 4.
2010 study indicating the instance of false rape (i.e. a person knowingly reporting a rape that did not occur with the express intention of causing harm to the accused) indicating 5.8% of rape reports are demonstrably false.
Another false rape study from the UK: 6% of allegations are false.
Another from the US Bureau of Justice Statistics: 8% unfounded (includes false and those that cannot be proven).
CDC - National Intimate Partner and Sexual Violence Study indicates 1 in 5 women have experienced rape or attempted rape.
2000 US DoJ report that fewer than 5% of attempted or completed rapes on college campuses are reported.
Also, a CDC report on male rape determining that 21% heterosexual males have experienced sexual violence other than rape (more than twice the number that will ever be accused of rape!).
IRMA rubric, which tests your biases against victims in cases of rape. Lower scores = more victim-blaming. It's an interesting tool to judge an individual's perception of rape myths.