No I have not been in a relationship that made me choose between my pet/pets & them - but my husband at times doesn't like my cats even though he brought some of them home. He has told me to find homes for them before even though I've had them for years and there all fixed. I explain to him that the shelters are full and in my area there killing about 7-9,000 cats a month. It's not like they are making anyone sick or anything like that. I even think that if he were to become allergic I would ask him to go on allergy meds. Not to be mean or anything & and yes people are more important than animals when it comes down to certain issues. My animals are part of my kids and they would be devastated if I abandoned them, or gave them away. So my husband doesn't win this one at all- instead he agrees and will be getting or building a cat house/shelter for the ones that would be better outside- and not just a little one but one that is the size of a small-med room w/heat in the winter. Everything deserves love and shelter.
If you have a low amount of animals or just one something should be worked out even if they have to take allergy medication, after all if you had a real child and you met someone they would have to accept that child with any problems or challenges that came along and could not tell you to give the child away.
God bless you!