Method to brew a large batch of iced tea without steeping in a plastic container

Stephie's answer covers a couple convenient options: there are large ceramic pots, and any stainless steel vessel can work. (Traditionally, metal has been frowned upon for tea brewing because it loses heat too quickly, and many people are particular about maintaining a consistent temperature during brewing. I think that concern is overblown, particularly if you aren't serving the tea hot.)

I'd also just challenge the assumption from the question that glass containers will shatter when used for brewing. It's really a question of the type of glass.

Glass vessels designed for hot liquids are usually produced from borosilicate glass, the same stuff used for most glass laboratory equipment. For example, borosilicate lab beakers are commonly available up to 5 liters, with pouring spouts as an option. The downside is most lab glassware doesn't have convenient handles. And beakers don't generally have lids, so storage in the same vessel is less convenient. (I have been known to brew tea in my 2-liter Erlenmeyer flask, which can be conveniently corked for storage; I guarantee it will get interesting looks from guests.)

I would, however, be careful with cooking glassware that is not specifically advertised as borosilicate glass. Much "pyrex" glassware, for example, has switched in the past few decades to a soda-lime glass formula, which is more susceptible to thermal shock breakage (though cheaper to manufacture). Ironically, you're often better off buying dedicated "professional" lab glassware for a cheaper price than the expensive non-borosilicate stuff often marketed in kitchen stores.

Personally, I've also found heavy-duty traditional canning jars to work fine for brewing tea. And they're usually available quite cheaply up to 2-quart size, with standard lids (including pourable flip-cap ones, if you look for them) so you wouldn't even need to change vessels from brewing to storage. (I'd be careful with the gallon-size ones, which often aren't built for standard canning and more susceptible to fracture.) Just don't "abuse" them or "beat them up" -- avoid metal stirring and cleaning utensils or rough handling, and periodically check for any sign of flaws.

Although it will generally take many thermal cycles before canning jars will crack, you can limit the stress by pouring a small amount of hot water in the bottom first (the most common breakage point in canning jars is around the bottom), "swishing" a bit, and then gradually filling the rest of the way -- or emptying that small amount and re-filling, sort of like "warming" a traditional teapot. Traditional ceramic pots are sometimes seen to crack over time too if you don't do this.