In the United States, at least, this is a pretty easy question.
There are of course plenty of reasons not to enjoy the e-mail. Perhaps the reader gets too much spam. Perhaps the reader is a fascist. But no one who accepts the American conception of free speech should have any trouble intuiting whether sending this e-mail was legal.
Communications in support of a political candidate are at the heart of First Amendment protection. Any suggestion that the e-mail violated the law because it communicated Barrett's electoral preferences is going to be a loser. Brinkman v. Budish, 692 F. Supp. 2d 855, 861 (S.D. Ohio 2010) ("First Amendment protection is at its zenith for core political speech which involves interactive communication concerning political change.” (quoting Buckley v. Amer. Const. Law Found., 525 U.S. 182, 186–87 (1999)).
The question of whether users consented is basically irrelevant. Americans do not need permission from the government or anyone else to communicate their positions on presidential elections, dog-catcher elections, or anything else. Watchtower Bible & Tract Soc'y of New York, Inc. v. Vill. of Stratton, 536 U.S. 150, 165–66 (2002) ("It is offensive — not only to the values protected by the First Amendment, but to the very notion of a free society — that in the context of everyday public discourse a citizen must first inform the government of her desire to speak to her neighbors and then obtain a permit to do so.").
Even if consent mattered, Expensify's users have presumably all agreed to its privacy policy, which alerts them that Expensify may send them "electronic newsletters" or "important notices," two categories of communications that are broad enough to include the e-mail in question. This also means that if Expensify is otherwise compliant with GDPR and other privacy obligations, there probably isn't much of an argument to be made that the e-mail violated any of those laws.
The fact that the e-mail is technically coming from a corporation does not matter, as corporate entities are allowed to take positions on political questions. Citizens United v. Fed. Election Comm'n, 558 U.S. 310, 342 (2010) ("First Amendment protection extends to corporations."). Nonprofit organizations are generally an exception, as they essentially surrender First Amendment protection in exchange for their tax exemptions.
One could attempt to argue that the e-mail is somehow an in-kind donation to the campaign. That argument would fail, but even if it were viable, that would not make the e-mail illegal; it would merely require Expensify to report it consistent with campaign-finance regulations.
