There was an answer here (now deleted) stating this in less cautious terms, but since NYT covered the issue on Nov 6, I think it's worth mentioning that one specific accusation was leveled at Vindman by retired colonel Jim Hickman, himself a very overt Trump supporter (prior to this disclosure) and QAnon fan. In turn, this accusation was retweeted/broadcast in various ways by the pro-Trump camp, including by Donald Trump Jr and also on Fox & Friends by Pete Hegseth.
The attack emerged late on Halloween night, when a retired Army officer, Jim Hickman, claimed he had overheard Colonel Vindman — a major at the time who was chatting with Russian soldiers during a military exercise — laugh “about Americans not being educated or worldly” and talking up “Obama & globalism to the point of uncomfortable.” Mr. Hickman said he took the major aside and reprimanded him.
Through his lawyer, Michael Volkov, Mr Vindman declined to comment.
Mr. Hickman, a former lieutenant colonel whose service record indicates he served in Afghanistan and earned a Purple Heart, at some point took an interest in QAnon. A review of his past tweets found more than 100 in which he recirculated or commented on QAnon-related theories, including hoaxes about Satanism and pedophilia, and until recently he had the hashtag #Q in his profile. Reached for comment, Mr. Hickman said he did not believe in QAnon but found it “interesting.”
“I do think it’s actually been pretty accurate on predicting a lot of things,” he said.
He has also tweeted strident pro-Trump, anti-Democratic themes, writing, “It’s incredible how evil the Democrat party is.” A week before going public with his story about Colonel Vindman, he retweeted a Trump supporter urging: “STOP IMPEACHMENT! STOP THIS COUP!” [...]
As the tale gained attention on Twitter, and received pushback from some who questioned it, a new Twitter account popped up with the name Thomas Lasch, tweeting that he had worked with Mr. Hickman and remembered the 2013 episode.
Mark Hertling, a retired general who was suspicious of the pair and contacted them through direct messaging, later tweeted: “They are who they say they are.” But he added that “LTC Hickman and I agreed to disagree on LTC Vindman and many other things.”
In an interview, General Hertling, who commanded the United States Army in Europe, said that a number of things about Mr. Hickman’s recollections did not add up, including his claim of hearing what Colonel Vindman, who was born in Ukraine, said to Russian soldiers.
“Vindman would’ve been speaking to Russian soldiers in Russian, not English,” he said. “Russians, when they come to these exercises, they don’t speak English — they take pride in it.”
General Hertling added: “I asked Hickman about that, and he said, ‘Well, they were going back and forth between Russian and English.’”
An effort to reach Mr. Lasch was unsuccessful. At his home in Homosassa, Fla., Mr. Hickman said, “All I want is the truth to get out.” [...]
But those who know and have worked with [Vindman] have provided a different account. They said that Colonel Vindman, then a military attaché, was assigned to meet with Russians and gather whatever intelligence he could.
He spoke to the Russians in Russian, did not denigrate the United States and reported everything he heard, according to a person briefed on the episode, speaking on the condition of anonymity because the colonel had not publicly testified. Colonel Vindman did not have dealings with Mr. Hickman in relation to his work during the exercise, the person said, and was not reprimanded for it.
Peter B. Zwack, a retired brigadier general who was Colonel Vindman’s commanding officer during the joint exercise, said he was skeptical of Mr. Hickman’s account.
“If there was something egregious that occurred, believe me, we would have had our ears rapped in Moscow,” said General Zwack, who served as the United States’ senior defense official and attaché to Russia.
“The bottom line is, where there are Russians in an exercise in and among our units and people, we have an attaché that coordinates with them,” the general said. “It’s all just a part of an attaché’s job.”
Attachés are expected to overtly collect information on what is happening in the country in which they are posted, as well as collect information from unsuspecting foreign officials through casual conversation. The allegations made by Mr. Hickman may simply describe Colonel Vindman playing his assigned role.
(The NYT article was also syndicated by The Independent in the UK.)
I wasn't able to turn up any more recent story than this that adds anything in terms of facts (either corroborating or disproving) to this matter.
And even if the event is true as recollected by Hickman, it doesn't prove that Vindman was a "never Trumper" in the usual sense. At best it would be an indication that Vindman had some positive things to say about Obama, which apparently is unforgivable (or proof enough) in some quarters (Donald Jr.) of a "leftist" inclination on Vindman's behalf.
Trump also accused other witnesses of being "Never Trumpers". So it's now apparently becoming a tradition to ask this in the hearings:
Like George Kent and William Taylor, whose testimony preceded hers, Yovanovitch was asked if she was a “never Trumper,” a charge some of the President’s allies have used to describe the witnesses who came forward. “No,” she answered firmly.
Kent and Taylor also denied it, the latter just as laconically as Yovanovitch.
Somewhat unsurprisingly, when Vindman testfied publically, he was (together with Jennifer Williams) asked the same question. And Vindman replied:
I'd call myself "never partisan".
The Washington Examiner disputed this self-characterization of Vindman, instead stating Vindman has registered as a Democrat in the past:
Vindman, a 44-year-old Army combat veteran who received a Purple Heart for injuries sustained during an IED explosion in Iraq in October 2004, initially registered as a Democrat in New York in 1994. He was listed as a Democrat at least as recently as 2009, according to public records. In 2012, Vindman registered to vote in Washington, D.C., but did not declare a party.
I could not verify this from other sources though.
(N.B. Mueller was a "true never Trumper" according to Trump.)