Really nonsense. It's true it might be more common due to all the additional modules and computers cars have now. If one goes crazy, it might drain your battery. But this is only in case of a failure. Edit: cold weather can accelerate that.
If it's 'weekend only', battery should be no problem. If sometimes you leave it a couple months unused, that might be a problem.
Depending on how ready you would like to be when you're going to use it, or the access you have to your car (is it far away or in your garage?) you could add a connector for a battery charger/maintainer (some of them have accessories for plugs you can leave permanently, see the NOCO GC002 for an example), and/or add a battery switch to easily disconnect the battery.
Warning: your radio might ask for a security code if it loses battery connectivity. Be sure you have it.
I don't have extensive experience with my current car bought last summer but 2 weeks in warmer weather definitely wasn't an issue.
I agree colder weather is always a bigger issue and at 1-2 months I'd definitely be thinking of a trickle charger if at all possible. An older car I didn't drive in the winter would definitely end up with a dead battery if I didn't keep it on a charger.
AGM batteries are a lot more durable than regular lead-acid. They can cost a bit more but for me the longer life, more resistances to issues if you do run them all the way down and their sealed, maintenance free nature makes them the first thing I swap out. Optima used to be the only commonly available batteries but Costco, for example, has AGM equivalents for just about every battery out there - you may have to order it and wait a few weeks.
They were also the original batteries used in Miata's since they give off a lot less hydrogen when charging. Since the Miata battery is in the trunk, and all lead acid batteries give off hydrogen when charging, and hydrogen in an enclosed space can also be rightfully called a bomb, having less of that is a good thing!
I must have had a bad run of big H8 AGMs in my Jag and Volvo. I think I've replaced about one a year on average. The Jag is very subject to parasitic drain and sometimes it just didn't come back from running itself out.
Did the Miata not come with a hole in the trunk floor for an exhaust hose for the battery? Both of my cars did...
If it's 'weekend only', battery should be no problem. If sometimes you leave it a couple months unused, that might be a problem.
Depending on how ready you would like to be when you're going to use it, or the access you have to your car (is it far away or in your garage?) you could add a connector for a battery charger/maintainer (some of them have accessories for plugs you can leave permanently, see the NOCO GC002 for an example), and/or add a battery switch to easily disconnect the battery.
Warning: your radio might ask for a security code if it loses battery connectivity. Be sure you have it.