While there might be certain delayed / detailed security checks due to belonging to some specific country, i wouldn't think of this necessarily being caused because of religion. Yes the name Muhammad might take longer, but likely not because of being Muslim, but rather because of being very common and hence a long list of possible name matches that CIC needs to ensure aren't related.
Canada is one of the best (if not the best) countries for immigrants. Unless one actually has something to worry about, things always get sorted out and immigration process isn't any different.
On that note, i am a Muslim with beard, came to Canada on a skilled job and latter got PR. Although my name is not Muhammad, two of my children's names are. We got our PR processed in among the fastest timelines (i believe it was 3.5 months)
We frequently travel to US as well - some times for work, some times for vacation and thankfully never have had any issues. Yes, probably the first few times they asked a bit more extra questions very politely. But that was about it.
And i am not alone. I know tons of people with similar situations. Those who have otherwise (poor) experiences, often have a part of story that they didn't put forward (in which they were guilty of something).
In my personal experience, this is far far better than irrational / double standardized behaviors that some of the most developed or developing Muslim countries show.
In the modern world, people value you by your deeds, quality of your behavior and work, not by the country of your origin or religion. I see that discrimination at its peak in the Middle eastern so called Muslim countries.
If we believe as Muslims that our values are equality, honesty, justice, kindness and others, i am pretty sure much of the west has adopted those, better than us and hence prospered much better as well. I certainly look up to them for those.