CTCI Chapter 1 : Palindrome Permutation
Nice implementation.

Here are a couple suggestions

collections.defaultdict

Intead of hashTable[i] = hashTable.get(i, 0) + 1, use collections.defaultdict

charcount = defaultdict(int)

for char in inputStr:
    charcount[char] += 1
actualCharactersInInput = len(inputStr) - charcount[' ']


collections.Counter

Or better yet, use a Counter:

charcount = collections.Counter(inputStr)
actualCharactersInInput = len(inputStr) - charcount[' ']


other

if actualCharactersInInput % 2:
    # odd number of chars
    return sum(count%2 for count in charcount.values()) == 1
else:
    # even number of chars
    return not any(count % 2 for count in charcount.values())