Is it possible for tourists to drive unhindered to the top of Mauna Kea on the big island of Hawaii?

Maybe according to Hawai'i magazine in an article from January 2020

In late December 2019, Harry Kim, mayor of Hawai?i County, struck a deal with protestors after ongoing negotiations to have the road cleared only for those wishing to visit the summit, however, no TMT construction materials would be allowed up. And on December 28th, 2019, the road was cleared of tents and protestors for the first time since its closing. This truce between protestors and government officials is expected to last until the end of February, after which negotiations will start up once again.

And then the West Hawai'i Today article from April 2020 says

Back in March, a camp that had stood for eight months in opposition to the proposed construction of the Thirty Meter Telescope on Maunakea was formally disbanded to ensure occupants’ safety as the pandemic intensified. However, a handful of people remain up there at any given time, along with a few abandoned tents and other detritus.

...

When the stay-at-home order is lifted — ostensibly on April 30, although that date could well be pushed back — Wong-Wilson said camp occupants will return to dismantle the rest of the camp.

Suggesting that the road is open to tourists.

However for a definitive answer I'd call the MAUNAKEA VISITOR INFORMATION STATION

Note that there are probably still COVID-19 restrictions in place, and that many sources say the that the last 5 miles of road to the actual summit require a true 4WD vehicle with a low range - and that using your rental car to get there will probably void your agreement. From the visitor center:

Visitors are advised that only TRUE 4-wheel drive vehicles with LOW range may travel above the VIS. About 200 yards beyond the station, the pavement ends and the next five miles are a steep graded-gravel road. Before proceeding visitors should consult their rental vehicle company or review their contract concerning visiting the summit of Maunakea. Many rental companies do not allow their vehicles on the summit even if they are 4-wheel drive, and if anything were to happen to your vehicle you would potentiially be responsible for all towing charges and repairs, which can be thousands of dollars ($$$$).