Having researched entry to Israel, I think it's mainly individuals who have converted to another religion (even Barbara streissands cousin who is orthodox had this issue although he went through teshuva), official members of the BDS movement, I suppose if one had membership in the JDL they would be denied, jews with criminal convictions depending on the offense, official ties to the Nazi party or terrorist organizations.
I don't think being associated with the jtf should prevent entry to israel , for example Meir kahane even though his party was banned in Israel I don't believe Meir kahane was banned entry to israel.
I know that Israel usually can impose a 10 year ban if you are considered a security threat and that happened to Noam Chomsky and Finkelstein.
There's been cases where known former neo Nazis have been able to visit Israel if they were truthful on a application when applying for a visa in countries where you have to apply for a visa. Perfect example was the jobbik party where the leader denied the holocaust and later found out he was Jewish and was able to visit israel.
Since JTF is a law abiding forum and many of us here do not advocate illegal activity, many of us support Israel through buying goods and what not I don't see any reason for issues to arrise.
I don't know chabadkahanists reason he was denied citizenship, for Chaim I've talked to him but will keep the discussion private unless he feels comfortable talking about it. Anyways those are then official reasons from what I understand, one of the biggest things Israel usually catches is if someone is hiding information or lies to a immigration officer that I believe this sparks a automatic 10 year ban.