My body my choice (False equivalence?)

Is the "My body my choice" response to getting the covid-19 vaccine a false equivalence fallacy regarding its original context of relating to abortion? Is it a Tu Quoque and a false equivalence fallacy? 

Actually, I think it is a fair "comeback." The problem is that "My body my choice" is a meant to be a sound byte and not an argument. There are too many exceptions to "My body my choice" that make it false/undesirable. For example, I can't strangle someone with my body. The anti-vaxxers are probably doing one of two things:

1) pointing out the problem with the "My body my choice" mantra.
2) being hypocritical and actually adopting the "My body my choice" manta - repurposing it for their own benefit.

Now, there is an argument to be made for a false equivalence if we expand the "My body my choice" mantra to a better argument. For example, it is "my choice" because I am not hurting anyone else and anti-vaxxers are causing massive harm to society in general. Granted, this would be the argument I would suspect one would make, and someone with a pro-life stance would argue that choosing to abort is causing massive harm (certain death to a human). So depending on your moral views abortion, this may or may not be fallacious.

It's not an argument as Dr Bo points out. This is extremely common in political discourse, actually - simplistic one-liners, or clichés, being used as if they were arguments. It's designed ultimately to dismiss a point of view without really reasoning through it properly.

We can parse an implicit argument, though:

P1) If it's my body, it is my choice whether or not to take the COVID vaccine.

P2) It is my body.

C) Therefore I don't have to take the COVID vaccine.

This is a valid argument, but doesn't justify not taking it - it only sets out guidelines for whether one can be compelled to take it or not. Furthermore, most anti-vaxxers modify C) to be 'therefore I shouldn't take the COVID vaccine' (which is a non sequitur; it does not follow that because something is not forced on you that you should decline it).

As Dr Bo also mentions, one could argue a false equivalence between vaccine mandates and abortion bans. But in order to start doing all of those lovely things, we must first get an actual argument out of the person.

It is just a bumper stick slogan. If you have a right to make a choice over your body in one case why would that not apply in the other?