Recently elected FIA president Mohammed Ben Sulayem reckoned there was "no way" he would use his platform at the top of motorsport's governing body to "impose my beliefs".
Ben Sulayem appeared to question Hamilton, Vettel and Lando Norris using their high profile to raise greater awareness on non-sporting issues.
When asked by GrandPrix247during the Monaco Grand Prix what motorsport "should not become", Ben Sulayem replied: "Niki Lauda and Alain Prost only cared about driving.
"Now, Vettel drives a rainbow bicycle, Lewis is passionate about human rights and Norris addresses mental health.
"Everybody has the right to think. To me, it is about deciding whether we should impose our believes in something over the sport all the time.
"I am from an Arabian culture. I am international and Muslim. I do not impose my believes on other people? No way! Never."
Ben Sulayem did appear to clarify his comments via Twitter.
On Wednesday he posted: "As a driver, I have always believed in sport as a catalyst of progress in society. That is why promoting sustainability, diversity and inclusion is a key priority of my mandate. In the same way, I value the commitment of all drivers and champions for a better future."
Those comments were put to Hamilton ahead of the Azerbaijan GP this weekend.
The Mercedes driver, who has previously said he wants to be "an ally" to the president in response to the clash over jewellery, suggested Ben Sulayem might have been taken out of context.
The seven-time champion added that regardless of the FIA president's views, he would not ease off in his activism and that all F1 drivers should be similarly "outspoken" on issues close to their hearts.
Hamilton continued: "That doesn't stop us from doing what we're doing. The sport is continuously growing. We have a bigger audience than ever… it continues to be an important platform to use our voices.
"Every single one of us here, within our industry, within our companies, can do more to speak out more on things to sparks more conversations.
"It's moving at a very slow pace. We need more people to utilise their platform. I encourage all the drivers to be more outspoken in the future about things they care about. I'm proud to see what Seb does and to be an ally of his."
Vettel, this month's cover star of Attitude magazine, followed suit.
After praising Hamilton's own efforts on diversity, for which the Brit will utilise his role as a producer on a forthcoming F1 film project led by Brad Pitt, Vettel said: "The topics that Lewis is continuing to raise, the issues Lando has been talking about and the stuff that I've been mentioning, I believe they are topics that are very important to be addressed.
"And they are bigger than us, bigger than a sport can ever be.
"It is important to mention those, express those and to raise awareness to make people aware that there's still lots of things that we can improve on."