There have been some questionable arguments put forward for why LoS seems to rub a lot of Castlevania fans the wrong way, but not all of of them should be discarded as obnoxious. It seems pretty clear to me that the reason is the high fantasy aesthetic that is notably more present than in the other games, up until the point that fans don't recognise associate the game with Castlevania anymore and thus say it's not like it.
Aesthetic is what binds a series and things like gameplay styles are often inrelevant. There are plently of series that include different game genres but are still recognised as being related to each other. You could make a shooter spin-off to a RPG series and still have it be faithful to its source material. That's why saying LoS is not a true Castlevania because it is inspired a lot by a different video game is a pretty shallow reason as already pointed out.
Considering LoS not a Castlevania games on the grounds of its prominent high fantasy aesthetic is a very valid reason, however. I suppose it's subjective but the developers themselves already seem to have admitted that the ties between their game and the rest of the series is very thin (they mentioned something about borrowing the "DNA" of the series and creating something new with it). So it seems to be a case of "how much is needed for me to consider something part of the Castlevania series"? Naturally, an universal agreement on that issue is impossible.