I know someone convicted of blasphemy law in his home country and he was rejected citizenship even though Canada does not consider blasphemy as a crime.
There is an error in this account, of some sort. Without attempting to explain the report, bottom-line is that a conviction for blasphemy based on elements of an offense which if done in Canada would not be an offense, will
NOT result in a prohibition that precludes a grant of citizenship.
The prohibition for a foreign conviction is explicitly based on a conviction for an offense which if committed in Canada, is an indictable offense. See
Section 22(3) in the Citizenship Act (this should link).
There are a variety of foreign convictions which would not constitute a prohibition. Some countries label a crime as fraud but the elements of the offense are essentially failure to pay a debt. That will not constitute a prohibition.
Such a conviction must, of course, be divulged to IRCC in the application, and IRCC will make its own assessment of the offense and determine whether it is or is not for a crime which if committed in Canada would be an indictable offense, hence a prohibition.
Also note, once a conviction which does constitute a prohibition is more than four years old, the individual will no longer be prohibited from citizenship (based on that conviction).
These are the ones who need to write explanation letters.
But police clearance as I understand from this forum is not required if we lived in Canada for the past 5 years.
The relevant period of time is FOUR years, four years prior to the date the application is made.
And a police certificate is required only if the applicant spent a total of 183 days or more in a particular country during those four years.
But as Joshua1 observed, if a refugee is a person who spent 183 or more days in a country during the preceding four years, and that was the country the refugee fled, obviously that individual would check "yes" in response to item 10.b, list the country, and explain that he or she is a refugee who fled that country and cannot obtain a police certificate from it.
Overall: there tends to be some confusion about how to answer item 10.b and having to submit a police certificate. Applicants can check "yes" in response to item 10.b, and should do so if they were in another country for 183 or more days within the preceding four years, and then give an explanation RATHER than submit a police certificate. And this is probably the best approach for any applicant who is confident he or she does not need to submit a police certificate even if the truthful answer to item 10.b is "yes." (That I apprehend many are in error when they believe they do not have to submit a police certificate is a separate matter; assuming they are correct, that does not necessarily excuse an untruthful "no" response to item 10.b as it is currently posed.)