The Dyer was part of the guildsmen which, in terms of hierarchy, was actually part of the trade class. They were one level up from the peasants, but one level down from the middle class.
The different levels of society (classes of society) during this period of time were as follows:
Aristocracy/Ruling Class, Clergy Class, Middle Class, Trade Class, & Peasant Class
The Dyer was a member of the merchant class. He was not a serf, dependent on his landlord for food and shelter, but he was still a peasant. If he owned the cloth dyeing business, he might have been a member of a guild, and if he was successful, he could have been wealthy for the time. If he was an apprentice, he would have been poor.
One disadvantage of being a dyer, however, was the smell. It is said that Elizabeth I decreed that all dyers had to live outside the city walls. Here is how the job is described in "The Worst Jobs in History":
We are reliably informed that a poor sense of smell, or no sense of smell at all, would be a definite advantage in this job, unless you are one of those who find the aroma of cabbage mixed with excrement and cat wee particularly appealing. A desire to live outside the city walls, whence you and all your fellow workers will be banished, would also be a plus.