Basically, for the former: No. Bloodstained isn't Castlevania. For the latter: Yes. We've had several Castlevania games since Order of Ecclesia.
I feel like those 2 statements directly contradict one another because of this:
There's a difference between one game playing like another and one game feeling like another. Personally the ost, the ambience, the fountains & lack of hearts and candles, the sound effects, the weight of the character, the combos, titan fights, the plot and final boss did not feel like Castlevania in LOS. It played like Castlevania for the most part( the character weight wasn't there and it held the player's hand too much, but the whipping and dagger throwing etc felt like Castlevania to me. As did the look of the main character, most of the environments and enemies (Werewolves, Vampires, Skeletons etc).
Bloodstained looks more like it will feel like the recent iterations of Castlevania (some like to call "Metroidvania" some don't)than LOS felt like classic Castlevania. Will it? Who the hell knows but we can only go by pre-conceptions for now. Based on that I would say yes it will feel that way because it's Iga's game.
In addition LOS is not Castlevania in the original series' sense. It doesn't share a lot of things with the original series, nor does it share the canon. We all know it had Castlevania slapped onto its title for profit reason$.
To summarise I don't believe one can say we've had several Castlevania games since OOE. Some may disagree with me but it's just the way I feel. If LOS is Castlevania to someone then BS sure looks a hell of a lot MORE like CV to me.