I've been trying to answer some of the old, highly-voted unanswered questions recently - which brings me to this attempt to answer one of my own. This has been one of the less fun topics to research; some of the concepts below are distasteful (but not explicit.)
Depends What 'Normal' Means
It turns out I accidentally hit on a key issue in the question title "Do rapists think rape is normal?"; I need to elaborate on a subtle distinction.
One issue is whether or not someone sees rape as a common or typical action for men.
Another issue is whether or not someone sees rapists as "normal" - e.g. agrees more with the statement that `Rapists are "normal" men.' than the statement `All rapists are mentally sick.'
Even though I do not show whether or not rapists see rape as more common than "regular" people, I will show below that they do NOT see rape as more normal than "regular" people.
I believe that it is a reasonable leap to think if they don't see rape as any more normal, they won't think that typical men are rapists, and thus this is counter-evidence for the claim made in the question.
The Evidence
Feild: Survey of 20 rapists and 1174 non-rapists
A key study in this area is by Feild:
Feild conducted surveys of many men (n=528), many women (n=528), many police officers (n=258), many female counsellors from a rape crisis centre (n=118) and a small number convicted rapists in a mental hospital (n=20).
Note: This was back in 1978. Society's opinions about women and rape have changed a lot in the past 30-odd years [Ref: Segal and Stermac (1985), that I will introduce further below].
The surveys asked a number of questions about their attitude to rape, and they were processed to give each person a score along a number of axes. That is, each person was given a rating according to a number of factors:
- Woman's Responsibility in Rape Prevention;
- Sex as Motivation for Rape
- Severe Punishment for Rape
- Victim Precipitation of Rape
- Normality of Rapists
- Power as Motivation for Rape
- Favorable Perception of a Woman After Rape
- Resistance as Woman's Role During Rape
Factor 5 is the relevant factor for this discussion.
Now, the variability in Factor 5 was partially accounted for by a number of determinants: Race (classified as Black or White), Marital Status, Knowledge about Rape all had a correlated with opinions on Factor 5. For some of the subgroups, some other variables were correlated: For regular Men and Women, their attitude toward women also played a part on their opinion on Factor 5. For police officers, their years of education played a part.
However, in the critical question of whether the grouping of the respondents into Citizens, Rapists, Police officers and Counsellors, it turns out Factor 5 is only statistically significantly different for the counsellors. That is, there was not a significant difference between citizens, rapists and police officers when it came to their attitudes about the normality of rape.

This is the key table from the study. It is tricky to understand. The important point to notice is that the numbers against "Normality of Rapists" under Citizens and under Rapists both have the same a superscript, indicating they are not significantly different (at p < 0.05).
Summarising the weaknesses of this evidence: it's about "normality" not frequency, it is from 1978, the sample size of rapists isn't huge and all the rapists were drawn from a mental hospital.
Nonetheless, it shows the attitudes of regular people and rapists were not significantly different when it came to the normality of rapists.
Segal and Stermac: Survey of 40 rapists, 40 other offenders and 40 non-rapists
I'm veering a little off-topic here, but I think this addresses some of the questions about the above study.
In a response to the Feild study, in 1984 Segal and Stermac attempted to address some of its shortcomings.
They increased the sample size to 40 rapists - importantly, they sampled 20 from a mental institution and 20 from a regular prison. They also only took respondents with an above average IQ (the reason for this is unclear).
To control for institutionalisation, they compared them against 40 non-sex offenders who had been imprisoned. They also compared to 40 citizens, but they were careful to match against equivalent men at the same low socio-economic status and intelligence.
They used a standard "Attitudes to Women" questionnaire. As an aside, they noticed that the community standards for the attitudes for women had changed a lot (become more liberal) since the questionnaire had been first measured, a decade earlier in 1973.
They were surprised by the results:
Contrary to predictions made, rapists at both centres did not differ from other offenders or from community based males, in their perceptions of women’s roles.
...
The findings reported are also consistent with research indicating little difference between rapists and
other low SES men on measures of social competence (Segal & Marshall, 1985; Stermac & Quinsey, in press). In fact, in the Segal and Marshall study, only high SES men differed significantly from rapists and low SES controls in their attitudes
towards women and on other indices of heterosexual social skill.
Now, this study has strayed even further from the original question. It is asking about attitudes to women, not if rape is normal or if rape is common. However, it is important because it supports the view that rapists do not have a vastly different attitudes to their non-sex-offending peers.
Feelgood et al: Survey of 25 rapists, 36 child molesters and 25 violent offenders
Another survey looking at the attitudes, coping skills and cognitive distortions of rapists was examined as part of a Masters dissertation by Steven Feelgood.
- Steven Feelgood, Franca Cortoni, Anthony Thompson, Sexual coping, general coping and cognitive distortions in incarcerated rapists and child molesters,Journal of Sexual Aggression, Vol. 11, Iss. 2, 2007, DOI:10.1080/13552600500073657
Rapists did not report more support for rape-supportive distortions than the violent offender comparison group. [...]
Evaluation of these comparisons was aided by effect sizes. The effect sizes reveal that there may indeed be differences between rapists and the comparison group with respect to cognitive distortions and sexual coping.
Again, rapists did not have strongly different views to their non-sex-offender peers.
The Conclusion
While this isn't a knock-down argument, it is strong evidence against the claim. In study after study, rapists do not have attitudes to rape that differ from similar control groups.
The evidence certainly isn't as clear cut in the other direction ("it comes out again and again") as the original claimant would suggest.