Does one transgress the aveira of ba'al tashchis by using disposables, e.g. disposable dishes, tablecloths, diapers? Alternatively is it a mitzva to use the real stuff instead of the disposables?

I can't really understand why it wouldn't be considered wasteful to use disposables?

i dont think one trangresses by using disposable goods- because baal tashchis is aquiring something, and squandaring it pointlessly. If for instance, you have food on your plate that doesnt taste good- you are allowed to throw it away- it doesnt hold any value for you. However, if you have made a dish of perfectly good food and go toss it in the garbage- that might be baal tashchis.

Disposable goods certainly serve valuable purposes for people these days. It saves time and energy that could be spent doing other things. As long as we put the products towards a useful action- it is not baal tashchis.

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I can't really understand why it wouldn't be considered wasteful to use disposables?

First of all, time is money too!! Also, think about the soap and water etc. that you'd have to use to wash the dishes, diapers, etc. Of course, we are also jaded, living in such a disposable society. But you have to choose whether you want dirty dishes, clean dishes and a tired mother/wife, or no dishes at all!

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you have to choose whether you want dirty dishes, clean dishes and a tired mother/wife, or no dishes at all!

A proof to this thinking is Shabbos 129a as paraphrased by Kollel iyun Hadaf
(d) (R. Chiya bar Avin): If someone let blood and got chilled, we may make a bonfire for him, even in summer [on Shabbos].
(e) They burned a chair of precious wood for Shmuel [after he let blood, for they could not find other wood], a precious table for Rav Yehudah, and a bench for Rabah.
(f) Abaye (to Rabah): Isn't this Bal Tashchis (being wasteful)?
(g) Rabah: It is preferable not to be wasteful with my health!