What is the max weight an MTB bicycle with a freewheel can handle until it starts putting high stress on the rear axle?

Axles break for various reasons - weight is only one of them. Miss aligned dropouts, flexing in the frame, tension of the QR all play a big part. Different axles with slightly different materials will also have an effect - some are stronger overall, some more brittle, some more prone to fatigue.

As you identified, riding style also affects the axle loading.

While the manufacturers probably put a number on this for their axles, I suspect its very conservatives and more reflective of there policy around warranty and brand value.

As far as regularly breaking freewheel axles, they are known to be weak compared to other options. A freehub wheel will probably solve your problem, but also check your frame dropout alignment.

So what is the max weight an MTB bicycle with a freewheel can handle until it starts putting high stress on the rear axle?

I can confirm that for someone who used to weigh 70 kg, the rear axle in an el-cheapo no-brand cassette hub (that doesn't have the right side bearing at the axle end in the manner Shimano cassette freehubs do) breaks in about no time (few thousand km). And that was on a bicycle that never saw a single jump, very gentle riding style and low-pressure over 40mm tires.

In contrast, I have never broken a Shimano cassette freehub axle even though my current weight is 110 kg and I currently use high-pressure 28mm tires.

Is there any way to reduce the chance of braking and bending axles?

Yes. Buy a Shimano freehub. If your current bike has a freewheel as opposed to a cassette, buy a cassette as well. This is most economical to do when you would need to change the rear sprockets anyway.

Unfortunately, changing a wheel hub is the second most difficult part in a bicycle to change (the most difficult being a frame). If you don't have wheelbuilding skills and equipment, you have to decide whether to learn the skills and purchase the needed equipment, or pay someone else to do the hub change, or simply purchase a new rear wheel with hub, spokes and rim in one package.

With a freewheel system, the bearings are closer together leaving a long stretch of axle unsupported past the right side bearings. It is common to bend or even break axles in these systems no matter what weight the rider puts on it. The heavier rider will probably notice more frequently bent axles that occur soon after replacement. Seven speed freewheel systems are especially prone to bent axles as the increased number of sprockets means there is an even longer section of unsupported axle which puts more strain on the vulnerable area.

Riding style will effect the frequency and severity of bent axles, but my experience has been even the most tame of riders of a freewheel system suffer a bent axle with great frequency. I replaced axles at least yearly on mountain bikes that saw mostly street use or well groomed trails. Solid axles provided no added protection from bending. It seemed to be worse--happen faster and more severely-- than the hollow axles of a quick release.

The move to a freehub system, which requires a new hub at minimum, will alleviate the frequency and severity of bent rear axles. In a freehub system, the right side bearing is moved inches more outside compared to a freewheel. This spreads the load out over a greater area and there is less unsupported axle past the bearing, diminishing the bending force due to effectively shortening the lever (the amount of unsupported axle past the right side bearing).

The most economical thing to do is acquire an entirely new wheel with a freehub installed. You'll require a compatible cassette as well since the freewheel won't go on the freehub. You don't mention the size of wheel your riding but it's likely to be a 26" based on the bike being a mountain bike with a freewheel system. If so, there is a great selection of 26" wheels to choose from and because of the mass movement to 29" & 27.5" wheels now days, prices for 26" wheels are generally low as demand has diminished.