I don't know what the trust does but I am unlikely to hate on them due to their members clearly being Spurs through and through. Anyone who doubts that should read the book We Are Tottenham.
Regarding Stadium MK, I think it is a logical decision from the club and it is only a League Cup tie. I don't think that us using that stadium endorses MK Dons over AFC Wimbledon although that is partly due to it being a few years after those issues.
All of that said, I'd hesitate to get annoyed at the trust for taking a stance in the direction of fairer ticket prices, fan owned clubs, and so on, even if the statement does read bad publicly and alienates some fans.
Just because they are less skilled in public relations does not mean they are a force of evil, or a voice that is unnecessary. If they have been found guilty of poor communication, I'd say them and the club are on level terms.
The club comes out better looking here but any time they don't there are not calls for the club to disband. So that is unfair expectation.