Isekai isn't parallel world though... it's literally a different world. Parallel world 平行世界 = different timeline that parallels (平行) to the original timeline, but the same world (世界); Isekai 異世界 = different (異) world (世界), timeline is irrelevant if time-travelling etc not involved.
Both are not mutually exclusive, which means we can have Isekai with parallel worlds that involve time-travelling, or non-Isekai Earth that involves time-travelling. Both are very much their own theme/genre that stands on their own.
(Edit) Earth time-travelling with parallel worlds, which it's not Isekai, generally is due to sci-fi events, could be due to fantasy events,
e.g.: Steins;Gate, Sengoku Komachi Kuroutan
Isekai time-travelling with parallel worlds (of that Isekai), which is Isekai because the perspective of the story is from non-native characters from Earth,
e.g.: Re:Zero, Yari no Yuusha no Yarinaoshi
Non-Isekai Fantasy (define: Fantasy as in having magics etc that don't exist in reality) world that the Earth is irrelevant/doesn't exist in the setting, is not Isekai,
e.g.: Goblin Slayer, Fairy Tail, Naruto
Non-Isekai Fantasy world that the Earth is irrelevant/doesn't exist in the setting, is not Isekai, but involves time-travelling, usually in the form of Reincarnation,
e.g.: Kouritsu Kuriya Madoushi, Hiraheishi wa Kako o Yumemiru
Earth with Fantasy settings and no time-travelling involved,
e.g.: Bleach, Yu Yu Hakusho, Digimon, Yu-Gi-Oh
Earth with Fantasy settings and time-travelling involved,
e.g.: Katekyo Hitman Reborn, InuYasha
(Edit) Earth with Non-fantasy settings and time-travelling involved,
e.g.: Sengoku Komachi Kuroutan
Reverse Isekai (which is Isekai genre/theme basically) where fantasy beings are transferred to our world but the story is just told from the perspective of Earth characters,
e.g.: Welcome to Japan Elf-san
Isekai is only Isekai from the perspectives of non-Isekai-natives, meaning that to people from Earth (transferred to Isekai or not), Isekai is another world that functions differently (like having magics etc, different universal physics etc) from Earth or the universe they are in (if different planet but still same physics etc, that's only sci-fi not Isekai). On the other hand, Earth is the Isekai from the perspectives of the fantasy beings from the world where characters from Earth are transferred to. Basically, it's like aliens to us are aliens because they are not from Earth, but to those aliens, we're the aliens from their perspectives.
So basically, just because alternate(parallel or not) timelines involved/created due to time-travelling occurred on the Earth in the story, it doesn't make that Earth to become Isekai, regardless of there are fantasy settings or not for that Earth (because all Earths in these fictions are Fictional Earths). Alternate(parallel or not) timelines of a world still belong to that world, and couldn't have existed if the original timeline never existed or changed. Isekai worlds don't need a non-Isekai original world (usually Earth of MCs) to exist in order to exist.
There's no harm that some people prefer to continue misunderstanding/mistaking/misinterpreting things that have definite answers due to their personal beliefs etc but remain that to themselves, but if they're just confused they could have just listened and learned. In so many cases (especially in BL series or BL comedy scenes in non-BL series), I see some people refuse to listen and insist on presenting their own opinions as objective arguments and use it as a way to trash the story/characters (or in this case, doing both that and implying that certain Isekai stories are generally bad just because they don't like some/many/all Isekai stories/characters), really shares similarities to behaviours of what we generally call, a hater, which the hater/cancel/anti-fandom cultures are really making many people exhausted and nobody wins from it. If this doesn't apply to you, great we all share the same hobby of reading mangas and hopefully mangas continue to excite us; but if this is applicable to you, there are better ways to express your opinions in a more constructive and compassionate way, so why don't we just get better and don't trash things that some other people like? Be a manga lover, not a manga hater! 😏