Eh, there are pros and cons to having a furry or non-furry mate. I've had both.
My non-furry mates have had more of a tendency to be embarrassed of animal costuming. They have also had more of a tendency to tease me a little bit about the whole furry and therianthropy thing, and they don't tend to take either seriously.
My furry mates haven't been great either though. One furry boyfriend was far more of a "furry fan," whereas I consider myself more of a furry lifestyler. We clashed drastically on a number of points, and he got just as embarrassed, if not moreso, than my non-furry mates of certain things like costuming and animalistic behaviors. As an example, that particular furry boyfriend was extremely embarrassed of me growling and running around on all fours, even though we were at the private residence of MY friends who didn't care.
Another furry mate was...extremely mentally and emotionally unbalanced to put it lightly, and he never really treated me right in our relationship.
My current mate of nearly three years is not a furry. He does tease me a little bit, but he's kind of light-hearted about it. He gets embarrassed of the costuming, but he grudgingly lets me wear things around the house, and he was nice enough to go to a furry convention with me one year. He also usually tolerates it when I wear my real fox tail, but I doubt he'd let me leave the house with my big fake fur ear and tail set. I did get out of the house in them once, but he only tolerated them that time because it was Halloween, and even then he teased me a little about it.