How do we know that parity is conserved in electromagnetism? Theoretically it is well established that parity is conserved in electromagnetism, that is the lagrangian is invariant under parity operation.
What I would like to know is what  experiments enforce this idea.
Suppose  we have a positive charge   at rest  and an electric field  pointing  to the  right  than the particle would accelerate to right. Now suppose that we inverted the electric field  that is the electric field is pointing to the left if in this case the acceleration would be still in the right direction would this be a parity violation ?
 A: Your example is classical. Assuming your charge is positive, the electric field and the acceleration are always pointing in the same direction,
$$
q \vec E= m\vec a.
$$
A parity transformation will reverse the direction of both $\vec E$ and $\vec a$, so when the electric field points left, a positive charge will also accelerate left. If it did not, that would be a parity violation.
Quantum mechanically, where this invariance of electromagnetism yields selection rules, you have that s states are parity even, and p states are parity odd. The most common EM interaction is an electric dipole transition, so
$$
\langle s| \vec r |p \rangle = \langle s|P P  \vec r PP|p \rangle \\
 \langle s|  P  \vec r P^{-1} (-)|p \rangle =  \langle s|  (-) \vec r   (-)|p \rangle \\ 
= \langle s| \vec r |p \rangle, 
$$
but
$$
\langle s| \vec r |s \rangle= - \langle s| \vec r |s \rangle \leadsto
\langle s| \vec r |s \rangle =0 ,
$$
and likewise $\langle p| \vec r |p \rangle =0$ , etc. This is the cornerstone of  most selection rules for atomic transitions, like Laporte's etc, controlling conventional physics.
It is only through violations of such parity rules, (finally established in atomic physics 40 years after parity violation was established in nuclear decays), that the minuscule effects of the weak neutral currents were detected in atomic physics, and because of these: the only way to see a needle in a haystack is  when the needle moves in the opposite direction to that of the haystack. Reviewed in Bouchiat, M. A., & Bouchiat, C. (1997), Parity violation in atoms,  Reports on Progress in Physics 60(11), 1351. Wieman et al. 1997 for weak Cs transitions.
