While Trump was a registered Democrat at the time who praised Kerry and opposed Iraq, he also praised Bush's tax cuts, said he liked both and was "undecided." Then a Trump-approved biography claimed he supported Bush. Although based on the narcissism of that paragraph (Kerry would have wanted Trump in his administration, of course, thanks to his godlike negotiating skills which could solve the Arab-Israeli conflict in 2 weeks), it's possible Trump just refused to acknowledge supporting a "loser."
https://www.buzzfeednews.com/article/christophermassie/cruz-claims-trump-supported-kerry-over-bush-in-04-theres-litBonus question: Cruz also claimed Trump supported Carter over Reagan in 1980, but I can't find any evidence of that. Do you think that's likely?