They have the same rights until you pass a law restricting their stock trading. Don't like it, simply don't become a senator.
They could still own stocks, either in a blind trust or in mutual/index funds.
But individual company stock trading would be prohibited.
Perdue facing his 3rd allegation of insider stock trading.
A number of senators got early CV briefing from Trump and then right away made trades that would seem to reflect that knowledge. Loeffler among them.
Avoid the appearance of impropriety, remove the temptation to cheat.