Twenty-six members of Congress at the time are still there, although nearly half have moved across the Capitol from the House to the Senate. It's worth pointing out that the 98th Congress, which approved the measure, was substantially more white than the current one (which is heavily white but still the most diverse in history).
We've broken down that vote below, comparing it to the current Congress. Vote tallies are from here and here.
The vast majority of lawmakers who voted against the measure were white, but one Hispanic member, Rep. Manual Luján (R-N.M.) voted against it.
Six current members of Congress were among those voting "no" in the 338-90 House vote and 78-22 Senate tally. Two, John McCain (R-Ariz.) and Richard Shelby (R-Ala.) moved from the House to the Senate in the interim. (Shelby was a Democrat when he voted against MLK Day.) McCain apologized for that vote when he ran for president in 2008.
Twenty current members supported it. They include Sens. Thad Cochran (R-Miss.) and Patrick Leahy (D-Vt.) and 10 who moved from the House to the Senate. That list includes Sens. Barbara Boxer (D-Calif.), Harry Reid (D-Nev.) and Pat Roberts (R-Kan.).
Notice how many more non-white members of Congress there are now. It's still not representative of the American population (and is actually diversifying much more slowly), but it's clearly less white.