Can we fix cells with glutaraldehyde and then stain with fluorescent phalloidin?

Yes, it is ok to fix cells with glutaraldehyde.

Keep in mind, the fixation method should be selected based-on experimental conditions. Fixing cells with formaldehyde, paraformaldehyde or glutaraldehyde will result in good actin filament staining using phalloidin conjugates such as Phalloidin-iFluor® 488.