Can face masks be removed during class at all?

Yes, but with limitations.

Metro Melbourne

The Restricted Activity Directions for Melbourne (effective from 27 October – 8 November) state that:

Only one person at a time may be exempted from wearing a face covering under the strenuous physical exercise exemption. e.g. the trainer leading the broadcast.

Reference on page 5:

Regional Victoria

The Restricted Activity Directions for Regional Victoria (No 10), (effective from 27 October – 8 November), state that:

All persons at an indoor sport or physical recreational training facility are required to wear a face covering other than when engaged in any strenuous physical exercise or where an exemption applies. All persons should ensure that duration of the ‘strenuous exercise’ exemption is as limited as possible.

Reference on page 4: