"openly moved" is correct and usable in written English.
You can use it to describe an emotional response to something. For example, "The audience was openly moved by the speech."
They are openly moving around in large numbers," said Yusufu Dama, who said he walked for two days to safety from Marte, a town near Baga.
Syria provided these groups with a safe haven and enabled them to recruit fighters who can now openly move between the Syrian and Iraqi battlefields, effectively erasing the border between the two countries.
At the Cambodian border, Bucklew witnessed the Vietcong openly moving supplies by sampan inside Cambodia, despite its neutrality.
Why it took so long to arrest Philippe when he was openly moving about in Haitian society is anyone's guess.
When the cast's nondancers, who wear their vulnerability openly, move across the stage in militaristic rows — it has the feel of an encroaching plague — the dancers, in orange, cut through like streaks of fire licking trees in a forest.
Years after the "War on Drugs" began, President Reagan, alongside First Lady Nancy, moved to openly affect the discourse on drugs, making substance use prevention into a national campaign.
Europe's pre-eminent financial centre is also battling to retain major investment banks – from Goldman Sachs to UBS – that are openly considering moving British-based operations to the EU.
Until recently the Zapatistas moved openly here.
In 1996, while 60,000 foreign troops patrolled Bosnia, the fugitive Karadzic moved openly between his home in Pale and the Prijedor area.
