Trump tweeted in 2014 that vaccines can cause autism. Has his attitude towards vaccines (assuming they haven't changed) affected US government policy on vaccines? If they haven't affected government policy, what impact can Trump have on US government policy on vaccines, directly or indirectly, at least with the congress that will exist subsequent to the 2018 election?
The president's main lever on this is that can appoint a cabinet level official known as the Secretary of Health and Human Services, who's department includes the Centers for Disease Control and Prevention (CDC).
In January of this year, Donald Trump appointed Alex Azar who has previously held an executive position in well a established pharmacutical company, and other positions within HHS under previous administration. While Azar is not without his critics, it seems unlikely he's going to shake-up U.S. policy on vaccinations. The general characterization of Azar has been that he is pro-vaccines.
There is nothing to worry about. It is unclear what you actually think a president can do to affect the availability of vaccines or prevent people from getting a vaccine if they want one. Speculating, I can only think of far fetch ways that the President can affect this issue. Frankly nothing I think of will result in masses of people not receiving vaccines if they wanted.
The president cannot stop federal funds from paying for vaccines. We can see that he does not have this power since he was unable to stop funding from: 1. Sanctuary cities, 2. Foreign countries receiving federal aid, 3. car companies receiving federal subsidies, 4. funds to support the Executive Orders of previous presidents specifically the DACA program. He cannot stop them since Congress is the one with the power of the purse
The president cannot order the armed forces to stop people from entering any location that provides vaccines. Aside from the logistical problem of placing a unit around every place that gives a vaccine, there is several laws that prevent the deployment of troops in the home country. We saw how controversial the deployment of a few thousand troops to the border. I suppose he could suspend the writ of habeus corpus as President Lincoln did but without the support of Congress, this is impossible.
The president cannot issue an executive order to prevent people from getting vaccines under penalty of law. Executive orders are not laws, they are orders to federal law enforcement agencies to enforce or ignore existing laws. The law has to exist before it is enforced or ignored so this will not apply. But suppose the order was given to tell law enforcement to stop people from entering locations that give vaccines, we have seen how orders can be blocked by the department of justice. For example the order to stop immigration from 7 specific countries for a temporary time was blocked because the judge felt the order was given in the spirit of racism because of something the president said. This order would fall by using the very tweet you provided in your question.
Medicaid and Medicare policy cannot be affected by the President as their authority comes from each individual state. While the federal government does provide funding and rule to regulate the funding, it is mostly congress that has that power and again, it is next to impossible that the President can order any funding to stop as I have already written.
I did think of a way for the president to do something about vaccine policy. He can use his personal fortune to bribe criminal elements to break some knee caps of those who want vaccines. With the whole gigantic span of conspiracy that some believe the current President is part of, I will leave it up to the reader to conclude how likely and effective this would be.