Vaccine and other healthcare stocks fell Friday after President-elect Donald Trump said Robert F. Kennedy Jr. is his pick to lead the U.S. Health and Human Services Department (HHS). But some analysts think the reaction may overstate the changes RFK might bring to the agency.

"Admittedly, it is difficult to evaluate the exact impact this appointment could have on the industry until we have more information on specific policy proposals and priorities of the incoming administration on healthcare and the drug industry," wrote J.P. Morgan analyst Chris Schott in a note to clients Friday.

Here's why there's concern: RFK Jr., a vocal skeptic of the drug approval process, will be able to select leaders of all the health departments under HHS, including the U.S. Food and Drug Administration (FDA), and Centers for Disease Control and Prevention (CDC), as well as the head of the Centers for Medicare and Medicaid Services (CMS).

"We are not surprised the sector has been under pressure on the potential for RFK Jr. having oversight of the various agencies within HHS...given his previous stated views on the industry," Schott wrote.

RFK Jr. has also been a vocal vaccine skeptic, questioning the need for the vaccine schedule required by schools and claiming, without evidence, they are not safe. That's stoked fears he will push vaccines off the market.

Vaccine stocks fell as much as 6% Thursday, and continued trading down Friday. Pfizer (PFE) and GSK (GSK) down more than 2%, while Moderna (MRNA) was down more than 5%. Other big pharma vaccine players like Merck (MRK), AstraZeneca (AZN), and Sanofi (SNY) were off by less than 1%.

But other healthcare stocks were affected too, which analysts believe was an overreaction.

One Jefferies analyst noted Belgium-based UCB Pharma, which makes epilepsy treatments, traded down 7% on the news of RFK's appointment, and that reaction "seems overdone."

Another Jefferies analyst, Michael Yee, said that RFK has not provided drastic solutions, but rather been skeptical of the regulatory process.

"To be clear — RFK has said he has no plans to 'take away vaccines' but the point is around sentiment, stance, and perspective - that impacts biotech investors' view of how FDA and other HHS issues will evolve (ie not accelerating drugs and pro-biotech)," Yee wrote in his note to clients late Thursday.

Mizuho's healthcare sector expert Jared Holz agreed, in a note prior to RFK's appointment when speculation was high.

"Believe that some of the early rhetoric around vaccines and otherwise is mainly noise as it relates to drug stocks with the exception of maybe covid-19 vaccine players (which are already mainly dead)." he wrote in a note to clients Thursday.