"OR" condition not executed during function run/Categorical is not ordered for operation max

I had found a helpful post on reducing the size of data frames using a custom function.

I have made one change to the function to fit the needs of my data frame because I have categorical variables within my data frame.

I added an "or" clause to the beginning if statement hoping that it would skip over any object as well as my categorical variables but when I run the function I still get an error.

The datatypes in data frame:

The function:

#copied function from kaggle
def reduce_mem_usage(props):
    start_mem_usg = props.memory_usage().sum() / 1024**2 
    print("Memory usage of properties dataframe is :",start_mem_usg," MB")
    NAlist = [] # Keeps track of columns that have missing values filled in. 
    for col in props.columns:
        if props[col].dtype != object or props[col].dtype != "category":  # Exclude strings and categories

            # Print current column type
            print("******************************")
            print("Column: ",col)
            print("dtype before: ",props[col].dtype)

            # make variables for Int, max and min
            IsInt = False
            mx = props[col].max()
            mn = props[col].min()

            # Integer does not support NA, therefore, NA needs to be filled
            if not np.isfinite(props[col]).all(): 
                NAlist.append(col)
                props[col].fillna(mn-1,inplace=True)  

            # test if column can be converted to an integer
            asint = props[col].fillna(0).astype(np.int64)
            result = (props[col] - asint)
            result = result.sum()
            if result > -0.01 and result < 0.01:
                IsInt = True


            # Make Integer/unsigned Integer datatypes
            if IsInt:
                if mn >= 0:
                    if mx < 255:
                        props[col] = props[col].astype(np.uint8)
                    elif mx < 65535:
                        props[col] = props[col].astype(np.uint16)
                    elif mx < 4294967295:
                        props[col] = props[col].astype(np.uint32)
                    else:
                        props[col] = props[col].astype(np.uint64)
                else:
                    if mn > np.iinfo(np.int8).min and mx < np.iinfo(np.int8).max:
                        props[col] = props[col].astype(np.int8)
                    elif mn > np.iinfo(np.int16).min and mx < np.iinfo(np.int16).max:
                        props[col] = props[col].astype(np.int16)
                    elif mn > np.iinfo(np.int32).min and mx < np.iinfo(np.int32).max:
                        props[col] = props[col].astype(np.int32)
                    elif mn > np.iinfo(np.int64).min and mx < np.iinfo(np.int64).max:
                        props[col] = props[col].astype(np.int64)    

            # Make float datatypes 32 bit
            else:
                props[col] = props[col].astype(np.float32)

            # Print new column type
            print("dtype after: ",props[col].dtype)
            print("******************************")

    # Print final result
    print("___MEMORY USAGE AFTER COMPLETION:___")
    mem_usg = props.memory_usage().sum() / 1024**2 
    print("Memory usage is: ",mem_usg," MB")
    print("This is ",100*mem_usg/start_mem_usg,"% of the initial size")
    return props, NAlist

Execution of said function:

props, NAlist = reduce_mem_usage(df)
print("_________________")
print("")
print("Warning: the following columns have missing values filled with 'df['column_name'].min() -1': ")
print("_________________")
print("")
print(NAlist)

I am not great at if statements/conditions so this might be a simple fix that I am just missing! Also, I just wanted to skip over the categorical variables because they do not take up a lot of space to begin with but if there is a better way to approach this problem I would love to hear it.