How can I filter out sunlight on a solar panel so that I can read a signal from a red laser?
A large solar panel like yours will have lots of capacitance. This means modulation will not work. You need a small sensor, with low capacitance, to avoid lowpass filtering your modulated signal into oblivion.

The laser tag I played used normal red lasers, but it was in the dark.

Most important is modulation. I presume you cannot put a sunshade on the target, if it is carried by a moving player.

Then, I suggest an optical bandpass filter, matching the optical wavelength of your laser. A bit of transparent red plastic would be a crude way to start for a red laser... Using a more narrowband filter would remove more of the sunlight of course.

An optical sensor sensitive only to your laser wavelength could work, too.