Based on the AZ federal murder case hinging on whether the judge was there just to say "hello" or there to discussion official business, I have to say since both are off duty in your scenario, they'd be treated the same.
Do Federal "public servants" get security guards paid for with tax-payer money, as opposed to other non-government "public servants" - say, those in the very dangerous mental health field - who must pay for their own security?
There's capitol police, but generally a protection detail isn't provided to congressional members, unlike for a president. Security can be requested and local police can provide security for an event. I believe in those cases the congressperson's office would pay.
Is this another example of a two class system of citizens, where the murder of those in the privileged class counts for more than those in the other class?
We're seeing federal charges because Congress decided to craft laws making it a criminal to kill federal employees while they're engaged in official duties, for example. The shooter will likely be charged for the murdered civilians under AZ state law.
Is this a violation of the Equal Protection Clause?
I don't know if it's been testing in court but it does make you wonder about the equality of victims. Is the judge's life really worth more or less only due to his job and his motive for being at that location? What does that say about us as a nation? It's a bit like "hate crime" statutes. I don't really like what it says about our nation but Congress obviously wanted to discourage people from being targeted sole based on their gov't employment.
The intent is to prevent the gov. employee from being the victim of anti-government violence. It isn’t unreasonable on the face of it if the attack is also an attack on the government or a policy. But it probably is not as limited as one would think.