A. Lots of people, for whatever reason (Lost Cause supporters or not) think that the 14th was illegally passed. The surest answer to the charge is that the amendment could have been challenged any time since 1868, and was not. The admitted blackmail that the United States exerted on the former Confederate states to ratify the 14th may have been questionable, but it is undeniable that the states all ratified it. There is also nothing in the Constitution that says that states or the federal government cannot exert pressure on another state to ratify an amendment. Again, the tactics may have been questionable in several cases, but not unconstitutional.
One argument is that some states rescinded ratification after they ratified and before full ratification. This has been the subject of some debate, but there has been a general constitutional argument that once a state ratifies an amendment, it cannot be unratified. Some focus on Ohio and New Jersey, which rescinded prior to July 9, 1868, the official date of ratification. However, Alabama, Georgia, and Virginia all ratified within a few months — even if these rescissions counted, which is debatable, the ratifications by Alabama and Georgia would have been enough to meet the requirement. The latest, then, the amendment could have been seen as ratified is July 21, 1868 instead of July 9, 1868.
Of course, at the time, the rescissions of the Ohio and New Jersey were noted, and rejected as invalid. The Secretary of State and Congress of the time listed both as having ratified and were included in the list of ratifying states. Now, these facts may not bolster your argument, but they do give you information that the other side will probably try to use. The other key point to note is that the Supreme Court has had, literally, hundreds of opportunities since 1868 to rule that the 14th is not a valid amendment but, indeed, it has used the 14th to greatly expand the protections of the people from government intrusion on civil rights.