Resistive and inductive load on same transformer?
Mixing resistive loads with inductive loads should cause no special concern. It is important to remember that the total load current for the transformer is not the arithmetic sum of the inductive and resistive currents but the vector sum. Inductive loads are rarely purely inductive, so you need to understand the effect of power factor.

What might be of more concern is the harmonic content that can be expected with any electronically controlled load. That should not be an issue with a zero-crossing temperature controller. It might be an issue with the servo controllers depending on the design. The transformer would need to be derated or have a sufficient "K factor" to avoid overheating due to harmonic content. The harmonic content adds a third dimension of vector addition. The inductive and resistive content helps in a way. More resistive and inductive current means the harmonic current is a smaller percentage of the total.

With various types of electronic power conversion equipment on one transformer there is always a chance of one system generating noise that interferes with other systems. Quality equipment should be designed avoid excessive emissions and accept reasonable emissions from other equipment. However evaluating the equipment may be difficult.