Syag, it hasn’t received a response, because I don’t believe it to be true. Particularly that last bit, as many Chabadniks say tehillim for everybody and most certainly do not discriminate at all cha”v.
However, there is some discrimination in official gatherings – Chabad does not officially attend the Siyum Hashas (although many Chabadniks do), is not part of Agudas Yisrael, did not take part of the huge macha against the giyus during Lapid’s gov’t (although Israeli CHabad did) and bythe internet asifa, there was some uproar when CHabad decided not to come, and then claimed they weren’t invited (or vice versa, not sure order of events there).
Furthermore, some shluchim, especially when they move into a kollel or modox community, feel the need to create their own infrastructure and fight with preexisting moisdois. When this happens, it’s a big brouhaha and brings bad feelings to lubavich. However, B”H, this is quite rare, occurs much more often by Mushrooms, and generally most Shluchim do integrate into existing communities and even send their kids to the already existing yeshivas, as per the Rebbe’s explicit instructions in the Igros (Yes, here he actually wrote this straight out, and not just through magic-asking).
However, not letting kids play by non-lubavichers? I never heard that. They’re certainly alot less segregated than other chassiduses
The biggest problem by Chabad, IMO, besides for Mashiach, is the need to constantly judge every gadol by their attitude to lubavich. Whenever a litvishe or chassidishe Rebbe dies, all the Chabad news sites will be judging them not on the basis of their greatness or their Torah, but rather what he holds about them. This practice does not exist anywhere in the Torah world. When the vizhnitzer Rebbe zt’l was niftar, no litvishe news site had comments like “he really respected Rav Shach” or “He held of our yeshivois”, rather they were all about his greatness and his qualities. Ma she’ein kein the the Chabad websites, where it was all about them.