Let me start out by saying I originally thought this was an equal protection issue but know I’m not so sure. Is it constitutional to unequally apply laws? Not necessarily civil rights or “give everyone speeding tickets” but let’s say three people are having an illegal sit in but only one is arrested. Can the person argue that they were singled out and that all three should have been arrested or if you observe 5 cars running a stop sign and a cop give a ticket to the 6th, can it be argued that it is unconstitutional as a unequal application of the law?
Aruged? Yes. Successfully? Not so much.
Yes, it’s constitutional, so long as the unequal application is not motivated by an impermissible racial or similar bias. Law enforcement and prosecutorial resources are limited, and courts will generally not inquire into the reasons why person X was charged while person Y was not.
SCOTUS says you can defend yourself on the grounds that prosecutors are trying you on the basis of race, but you have to establish that race-conscious prosecution is occurring, at the very least by showing that similarly situated defendants of other races were not prosecuted.
The same is generally true of interactions with law enforcement. You have to demonstrate an impermissible motive for pulling your car over but not #5.
What if a whole bunch of cars are driving at 25 mph over the limit, and among them you are driving at 10 mph over the limit – and the cop pulls you over and gives you a ticket? Do you have a defense in demanding that the officer explain why he pulled over a 10 mph speeder in the midst of a bunch of 25 mph speeders?
I read such an anecdote once in that journal of All True Anecdotes, Readers’ Digest. The cop explained: That was the only car I could catch.
Case dismissed.
There was another anecdote which I believe was also in the Readers’ Digest in which the cop asked the driver “You ever go fishing?” “Yes.” “You ever catch them all?” Citation issued.
You ran the stop sign and that’s illegal. Be a mensch and take responsibility for your actions.
They were going 25 over the limit, you were going 10 over?
Not only were you speeding, but at 15mph less than the rest you were also impeding the flow of traffic. So 2 tickets for you! 
Very true. Also an assertion of one’s constitutional rights may be grounds for selective prosecution. For example, say a police officer sees 5 guys loitering in the park and tells them to move along. One of the guys politely asks, “Don’t we have the right to peaceably assemble here?” The cop cuffs him and asks the other four guys if they would like to move along or go to jail with their friend.
The arrestee, at least in my state, has a colorable ground for selective prosecution: He was only arrested for attempting to assert a right; the officer didn’t care about his loitering.