This is very concerning. Both the situation of mamzerim and also if they allow converts, as I read they do...they would not be a giyur al pi halacha...so then you would have Karaite Jews who are mamzerim and then those who would not really be Jews. Although would they not naturally filer each other out (a male mamzer who has a child with a gentile woman would not have mamzerim children yet they could convert giyur al pi halacha in a beis din as non-mamzerim).
Anyways, besides the complications on their line....would karaite Jews not be considered tinoq shenishbah?
Also, once the video was over (the first video) and I saw something more concerning...that the video labeled "convert the world to Judaism"...that is a subject for a different topic but it seems that no one wants to talk about the particular rabbi who makes those videos all over YouTube.