Displays of patriotism were evident at parades and hot dog eating contests, even at a time of deep political divisions among Americans.

Mr. Chestnut, who was barred last year over an endorsement deal with a vegan-meat company, and Miki Sudo easily won their respective contests but did not break records.

There are serious questions about the wisdom and durability of President Trump’s policies, but on his terms, he can point to a string of accomplishments.