Musk on Thursday denied a report by Business Insider that he sexually harassed a flight attendant on a private jet in 2016, calling the person who made the claim a liar.
The previous day, the Tesla chief executive, in the midst of a contentious effort to buy Twitter Inc, said he would now vote Republican instead of Democrat and called the Democrats a "party of division and hate."
Tesla also was cut this week from the widely followed S&P 500 ESG Index, which an index executive said was due to issues including claims of racial discrimination within the company and crashes linked to its vehicles.
Musk responded by calling such ratings around environmental, social and governance (ESG) issues a "scam," and questioned how the index could drop an electric car firm while adding oil and gas producers.
Tesla could not immediately be reached to comment.
While Musk has made attention-grabbing headlines before - once calling one critic a "pedo guy" on Twitter - the latest controversies again raise the question whether his outspokenness will tarnish his likeability. And - since Musk is so closely tied to Tesla - whether that will that hurt the carmaker's sales, especially in California.
The left-leaning state is Tesla's largest market, accounting for nearly 40% of the company's U.S. retail registrations last year, according to Experian data. Tesla sales in California were up almost 70% in the year and it had a 6.5% share of all vehicles in the state, according to the California New Car Dealers Association.
#BoycottTesla was trending on Twitter on Friday and several people claimed they were canceling their car orders.
"In the past, I admired him for working to build a green business that's transformational in energy use. But he is sadly becoming divisive as an attention seeking troll and I no longer trust that he is dedicated to the quality of his products. I will cancel my Tesla order," said J Yeh, a Twitter user who describes herself as a lawyer who has lived in several cities including Los Angeles.
"You lost a potential customer," a Twitter user named Ute Bauer from Germany said, adding in German: "To anyone reading this, cancel your orders."
Reuters was unable to confirm if any Tesla orders had been canceled.
Many institutional investors may stand by Musk no matter what given the company's strong performance, but that doesn't mean some aren't frustrated.
"They're doing a lot of good things," said Taylor Ogan, CEO of Snow Bull Capital, which owns Tesla shares. "It's just disappointing when that is tainted by Elon Musk's antics. Elon Musk is the best thing for Tesla and the worst thing for Tesla."
One Tesla employee, who asked not to be identified, voiced frustration that Musk's efforts outside Tesla appeared to be hurting the carmaker's stock. "The company needs to do something to address the issue," he said.
On Friday, Tesla shares dropped almost 9%, knocking about $66 billion off of Tesla's stock market value and putting the stock at its lowest level since last August, with analysts citing "distraction risks" from the Twitter deal. Musk assured people on Thursday Tesla was constantly on his mind.
If discussion around water coolers at work focused on the sexual harassment claim against Musk rather than Tesla products, the end result could be "corrosive" for the Tesla brand, said John Smith, a former group vice president at GM who ran global product planning.
Tesla and SpaceX employees also could become "a little bit rattled and angry" because of Musk's anti-Democratic party comments as technology company staff in California tend to be more liberal, said Jason Stomel, founder of tech talent agency Cadre.
Bill Nelson, administrator of NASA, which relies on Musk's SpaceX to fly its astronauts to space, told Reuters on Thursday that Musk has a strong team of executives at the spacecraft maker and the agency's partnership with the company was "going without a hitch."
And Musk still has plenty of fans online. Twitter user @JVega103 said he was a Republican who owned a Tesla and just signed up for Tesla solar panels. "Thanks for everything you do," the user tweeted.
That left some industry observers wondering whether Musk and Tesla would simply shake off these latest controversies, as they have in the past.
"Is Elon Musk now crazy, or crazy like a fox? He has earned the benefit of the doubt as he is often playing chess when the rest of us are playing checkers," Northwestern University professor Erik Qualman said. "As Musk himself on 'Saturday Night Live' famously stated, 'What, did you think I would be normal?'"
(Reporting by Hyunjoo Jin in San Francisco and Paul Lienert in Detroit, additional reporting by Tina Bellon in Austin, Texas; Noel Randewich in San Francisco, Joey Roulette in Cape Canaveral, Fla; Ben Klayman in Detroit, and Nivedita Balu in Bengaluru; Editing by Peter Henderson and Rosalba O'Brien)
By Hyunjoo Jin and Paul Lienert