How hot / humid does it have to be for cycle touring to become unenjoyable?

The exact answer depends on the individual, but there are some general aspects worth noting.

Sweating

The only way for humans to cool down is through sweat evaporation (as this article explains). If the air is also very humid, sweat will not evaporate as effectively because the surrounding air is close to being saturated with water (56% is normal, though). If the air is very dry (below 30% for example, as in desert conditions), sweat will evaporate too quickly, causing dehydration.

There are also certain health disorders that could affect one's ability to sweat, such as Hypohidrosis, which may lead to quicker overheating.

Also, through sweat you lose sodium and other minerals, which you need to intake by means of foods and drinks, to avoid problems such as Hyponatremia.

Fat or thin

In this article it is stated that for both dry and humid heat, being thin and having little body fat is better. This is because thin people have a higher body surface area/volume ratio (you can calculate your exact SA÷V here) and can radiate heat better.

Brainiac did an experiment (not the most scientific one):

My personal experience

I live in Southeastern Europe, where are four seasons, and temperatures during summer are quite high, around 30C peak. I am tall and thin, with a SA÷V (surface area/volume) of 3, so better suited for hot weather, according to the linked articles. I never had overheating problems, but my skin is very white and I get sunburnt very easily.

On Jul 11th, 2020 I did a 13 hour ride on a hot day (my previous longest being 7h). The peak temperature that day was 29C, and 50% avg. humidity. I did not have major problems with overheating, but it was uncomfortable, I consumed about 8 liters of water and electrolyte drinks, got slight sunburns even with suncream, and was a little dizzy in the evening, but fine the next day.

Conclusion

If you are rather chubby, had any health issues in the past (not only related to overheating), and never did a long ride on a hot day, then it will be very tough, unsafe and risky.

If you are thin, healthy and fit, never had problems with heat, have good experience with bike touring, are very prepared (with electrolytes, sun protection, good info regarding location of water sources and rest stops, have emergency plans, etc.) you take it easy at first (e.g just cycle 6h in the morning, the first day), and you avoid long routes through the middle of nowhere, then you have better chances at succeeding.

I was out in 28C and 50% RH yesterday, not touring, but comparable: a century (160km) at a fast touring pace, laden by the standards of a day ride, and with a brief swim break in the afternoon. It was hard work (much harder than it would be 10 degrees cooler), but still enjoyable. You have to plan on being able to obtain water. I got through about 4 litres, and have reached 9 litres in the past on hot 200km rides. Especially for multi-day riding, like touring, will your appetite survive the heat? I tend not to eat enough on a long day's ride, if it's over about 25C by lunchtime, though if you can buy ice cream...

Road conditions matter - dropping into a wooded valley from an exposed hillside is a great relief. How likely is shade?

If you can avoid the hottest part of the day, that helps, but many areas lose heat slowly, so avoiding the heat means doing most of your riding in the morning, resting or sightseeing in the afternoon, and maybe doing a little in the evening. But does this fit with your target daily distance? Is there a shady (and pleasant, with food/water) place to rest out the heat?

Clothing is tricky. Clothing for sun protection keeps the wind off, so even if it didn't make you hotter standing still, it would going along. Arranging clothing to allow more airflow means it flaps in the wind and makes you work harder.

Guessing at your route as Sydney->Brisbane (but not along the coast), and quickly checking the map, the road passes through plenty of towns, so places to stop even if most are small, however street view suggests you'd be riding in unbroken sun for long periods - I've been known to stop and drink under every rare tree in that case.

This is a very subjective question, but I believe there is at least an upper bounds on the temperature most people can tolerate while cycling for long distances. Somewhere a little higher than 37C is where the wind stops cooling you and starts to heat you while you are dry. I've found that if you are cycling at times like that, you need to cool off regularly with some cold water, splash some on your body if the air is dry, or take a break.

I've not studied any of the science at all and I am only speaking of my personal experience touring thousands of km in the summer through the very humid southeast US and great plains regions. Hopefully you may find some of it useful or at least entertaining.

As a general rule I would get up at or before sunrise and cycle until 10-11 am, sometimes later, depending on the heat and humidity. I always stopped if the temperature reached 35 (95F) even if I seemed to feel okay. And even if the temperature didn't get that high I would usually stop at some point during the midday hours anyway, and start cycling again around 3-4 pm when the day started cooling off. On some really hot days (above 38/100F) I might not have started again until 6 pm or later.

On one particularly hot and humid August day in South Carolina, by 8:30 am it had already reached 31 (88F) and I wasn't feeling so well due to the heat and 80%!! humidity so I stopped at a roadside rest area for a few hours (the toilets were air conditioned!) then checked into a nearby hotel as soon as they allowed check-in. I only rode 29 km that day, almost all of it before 8:30 am.

I would stop anywhere that there was shade or air conditioning available: covered picnic tables in public parks, Starbucks, etc. Once, when there was nowhere more suitable to stop within a short distance, I just parked the bike next to a tree at the roadside and sat under it for a couple of hours.

On days when the temperature didn't exceed 30 (86F) all day, I generally cycled through the whole day, with only short breaks of 15-30 minutes here and there. This is about the highest I think the temperature can get with full humidity and still make an enjoyable ride. Still a lot of sweating involved, and thus a lot of drinking water, but it wasn't a really oppressive sort of humidity at those lower temperatures.

Some things I would think about if I were planning this tour:

If you don't routinely cycle more than a few km/day, you might need as much as a couple of weeks to be able to cycle more than 30-50km comfortably. Take it very easy the first few days in this case.

When you're looking at climate data, keep in mind that when they say "average" they mean average, and on any given day you are likely to experience conditions better or worse than that. The climate data I saw for Brisbane and Sydney for November and December suggests to me that riding on most days would be fine, but I expect if I were riding it, I would be stopping during the midday a lot, to wait for the heat of the day to pass. Sydney being a bit cooler on average, I would also consider doing the tour southbound.

If you ride along the coast you should expect the humidity to be higher, as during the summer the predominant wind is blowing in off the ocean.

Remember that the better you are able to keep yourself fed and hydrated, the better you will do. Don't be afraid to stop to eat and drink. It's a tour, not a race. On that note, don't be afraid to stop and look at the scenery. You may never pass this way again.

There are already a lot of good answers here, so I'll keep this fairly short.

An important number to pay attention to is the dew point or the heat index. The heat index is essentially a combination of the dew point and temperature to get the "feels like" temperature.

A good rule of thumb is that a dew point below 15 C is comfortable. Between 15 and 20 feels muggy, and your sweat won't evaporate very quickly, so even low intensity effort will leave you damp. Once the dew point gets above 20 C, most people are uncomfortable exercising for extended periods, and your clothes will be very wet from the unevaporated sweat. If the dew point gets to 25 C, exercising outdoors is dangerous, as your body will not be able to cool.

Your example of air temp of 30 C and 55% RH gives a dew point of 20 C, so you're getting into uncomfortably humid. In addition to the concerns about hydration, expect to be wet all the time, so make sure your clothes are comfortable to wear when soaking wet. Wet socks leave your feet more prone to blistering, so make sure your socks and shoes fit well and don't have any friction points. Also keep in mind that if you are camping, your clothes won't dry overnight with that much humidity, as the relative humidity will likely be near 100% in the early morning when you start out.