Regular expressions are very useful if you want case-insensitivity (and of course all the power of regex).
my_string = "Mary had a little lamb"
# simplest solution, using count, is case-sensitive
my_string.count("m") # yields 1
import re
# case-sensitive with regex
len(re.findall("m", my_string))
# three ways to get case insensitivity - all yield 2
len(re.findall("(?i)m", my_string))
len(re.findall("m|M", my_string))
len(re.findall(re.compile("m",re.IGNORECASE), my_string))
Be aware that the regex version takes on the order of ten times as long to run, which will likely be an issue only if my_string is tremendously long, or the code is inside a deep loop.