If you take racism as the believe of differences between humans of different areas/countries/appearance, then definitely. While it becomes pretty obvious, if you look at the descriptions of Barbarians compared to the Romans, for example, you can even see such concept between Romans and Greeks. A very good example is the latin word pergraecari, which literally translates to live thoroughly like the Greeks, but means to live on the fat of the land (hopefully the right choice in my english dictionary), or to be lazy, so in anyway you don't live with discipline and get something done. So you can see, that the Romans attributed lazyness and lack of self-discipline as a special Greek characteristic, that separates them from the Romans.

For Barbarians, it is quite common to see them described as physically superior, but always lacking discipline, being dumber than the Romans, lacking technical knowhow, being easily impressed by the superior Roman knowledge and creativity. For this Caesar's bellum gallicum is a good example.

I can't look up more in detail right know, so i hope, that gives you an overview and idea. Maybe someone else will find this and can give some more detailed examples, especially on the Greek view, because i don't know very well about that. However, if you have further questions to my post, I will try to answer them.

This is a complex issue, to say the least. The book you mentioned, Benjamin Isaac's The Invention of Racism in Classical Antiquity, is a somewhat controversial book that has received mixed reviews from scholars. The basic premise is as you described--Greeks and Romans held what he termed "proto-racist" views which positioned themselves over other groups of people on a basis of language, culture, geography, and other means. The problem here is what is meant by "proto-racist." Isaac's definition of it does not seem to distinguish it from just racism in the modern sense, as some reviewers noted. Also, modern injections of the term "race" into antiquity has always been fraught with anachronistic pitfalls. There is no 1:1 equivalent to "race" in ancient Greek or Latin. There are words like ethnos, genos, laos, etc. which mean some sort of group collective, but Greek authors themselves used these words in many different ways in different contexts. Simply put, there was no intellectual consensus for what these words meant. Thus, it is hard for us today to come up with a single racial theory for the ancients.

Nonetheless, for the most part, it does seem that Greeks and Roman authors did have believe in some sense of superiority over many of their neighbors. Each author, however, exhibited this attitude to varying degrees and in different manners. And, as Erich Gruen argues in Rethinking the Other in Antiquity, some intellectuals did not feel any sort of cultural or ethnic superiority over people unlike themselves. This may have been a minority opinion in antiquity, but such opinions nonetheless existed.

I think the main takeaway is that people in antiquity held as many varying opinions towards non-Greeks and non-Romans as people do today. The ancient Mediterranean consisted of a huge swathe of different cultures and peoples. Some people were more tolerant of others than others, and some were most assuredly discriminatory against people different from themselves. Whether we want to use the word "race" is up for intellectual debate though.