Concatenate dataframes and remove duplicates based on multiple columns value

Use pandas.concat to concatenate a list of dataframes. Then, use pandas.DataFrame.drop_duplicates() to drop the duplicate records. The pandas.DataFrame.drop_duplicates() function has a parameter called subset that you can use to determine which columns to include in the duplicates search. Here's how to do it, using the example you gave:

import pandas as pd

data1 = {
    "first_column": ["1", "2", "2", "2"],
    "second_column": ["1", "2", "2", "2"],
    "key_column1": ["1", "2", "2", "6"],
    "key_column2": ["1", "2", "2", "1"],
    "fourth_column": ["1", "2", "2", "2"],
}
df1 = pd.DataFrame(data1)

data2 = {
    "first_column": ["1", "2", "2", "2"],
    "second_column": ["1", "2", "2", "2"],
    "key_column1": ["1", "3", "2", "6"],
    "key_column2": ["1", "5", "2", "2"],
    "fourth_column": ["1", "2", "2", "2"],
}

df2 = pd.DataFrame(data2)

df_combined = (
    pd.concat([df1, df2])
    .drop_duplicates(subset=["key_column1", "key_column2"], keep="first")
    .reset_index(drop=True)
)
df_combined

The above code outputs the following:

If you want to wrapt it all inside of a function here's how you might consider doing it:

from __future__ import annotations
from typing import List
import pandas as pd


def concat_no_dups(*dfs: pd.DataFrame, key_columns: List[str] | str | None = None) -> pd.DataFrame:
    """
    Concatenate dataframes together and drop duplicates based on equality of
    selected columns.

    Parameters
    ----------
    dfs : pd.DataFrame
        A sequence of dataframes.
    key_columns : List[str] | str | None, optional
        The columns to use as keys to drop duplicates.
        If no list, or column provided, it uses all the columns
        from the concatenated dataframe, to search for duplicates

    Returns
    -------
    df_combined : DataFrame
        The concatenated dataframe with duplicate rows removed.

    Raises
    ------
    KeyError
        If one or more keys from `key_columns` do not exist in the dataframe,
        obtained after combining all `dfs` together.

    Examples
    --------
    >>> import pandas as pd
    >>> data1 = pd.DataFrame(
        [['a', 12], ['a', 15], ['b', 19], ['c', 18]],
        columns=['key', 'value']
    )
    >>> data2 = pd.DataFrame(
        [['a', 16], ['a', 10], ['b', 13], ['e', 19]],
        columns=['key', 'value']
    )
    >>> concat_no_dups(data1, data2, key_columns='key')
      key  value
    0   a     12
    1   b     19
    2   c     18
    3   e     19
    >>> concat_no_dups(data1, data2, key_columns=['key', 'value'])
      key  value
    0   a     12
    1   a     15
    2   b     19
    3   c     18
    4   a     16
    5   a     10
    6   b     13
    7   e     19
    >>> concat_no_dups(data1, data2)
      key  value
    0   a     12
    1   a     15
    2   b     19
    3   c     18
    4   a     16
    5   a     10
    6   b     13
    7   e     19
    >>> concat_no_dups(data1, data2, data1)
      key  value
    0   a     12
    1   a     15
    2   b     19
    3   c     18
    4   a     16
    5   a     10
    6   b     13
    7   e     19
    """
    df_combined = pd.concat([df for df in dfs])
    if key_columns is None:
        key_columns = list(df_combined.columns)
    elif not hasattr(key_columns, '__iter__') or isinstance(key_columns, str):
        key_columns = [key_columns]
    missing_keys = pd.Index(key_columns).difference(df_combined.columns)
    if not missing_keys.empty:
        raise KeyError(
            f"The following key columns weren't found: {list(missing_keys)}. "
            f"Available columns: {list(df_combined.columns.astype(str))}."
        )
    return df_combined.drop_duplicates(subset=key_columns).reset_index(drop=True)