Is it a requirement to have a vehicle in the Army Reserves?

PVT (Join to see) The requirement is to meet requirements of battle assembly. How you do it is on you. If you don't meet battle assembly requirements you can be separated from the Army Reserve for non-participation.

AR 135-91
3–1. Satisfactory participation in troop program units
TPU Soldiers are required to participate in at least 48 scheduled inactive duty training (IDT) periods, and no less than 14 days, exclusive of travel time, of AT. Satisfactory participation is defined in paragraphs 3–1a through 3–1c as— a. Attending all scheduled IDTs unless excused by the unit commander or granted an authorized absence. Soldiers present at a scheduled IDT period will not receive credit for attendance unless they are wearing the prescribed uniform. They must also present a neat and Soldierly appearance and perform assigned duties in a satisfactory manner as determined by the unit commander. Soldiers who do not receive credit for attendance for any of the reasons noted above for any IDT period will be charged with an unexcused absence for each such period as prescribed in chapter 4,
section III.
b. Attending and satisfactorily completing the entire period of AT unless excused by proper authority. c. Obtaining a unit assignment during an authorized absence (see chap 4, sec IV).

Implied task: you must get there. Plane, train, automobile, conveyor belt, pogo stick, matter transport: your problem.

It is a requirement to be at drills, how you get there is the SM's problem- not showing you will definitely by a problem for the SM.

PVT (Join to see) Is he in trouble for missing drill? If so, he needs to find a way to get to drill on time in the right uniform.

How do you get to your regular job?

How do they get to there McDonald's job when they are not at drill?

No, it is not a requirement to have a car to be in the army reserve.

At times it makes things easier.

I assume this soldier is at least 18 years old and is leagally an adult. There is no reason they shouldn’t have some form of reliable transportation to get them back and forth to work. Army Regulation or not, there is a valid reason for this persons command to want everyone to have transportation. If that unit is called up for a mission, the last thing their commander and NCOs are going to want to hear is “ I can’t come, I don’t have a car.”

General rule in the military, if they require it they must provide it.