Generally speaking, this is NOT a good idea.
If both your fischer and your peachface are pets, then keeping them in the same cage may cause them to become less tame to their human companions. Lovebirds that like each other will bond strongly with each other if they live in the same cage together. When they create this pair bond, they depend on the other bird for company and no longer need their humans for companionship like they used to. A “pair bond’ can be created regardless of the sexes of the birds involved, and peachface lovebirds can bond just as strongly with fischer lovebirds as they can with another peachface. This is especially true if these are the only two birds in the house.
Lovebirds each have their own individual personalities, and there is definitely always a chance that two lovebirds will NOT like each other. This is true even if they are the only two birds in the house. Throwing two birds in the same cage together is like putting two random humans in the same house together and expecting them to live peacefully. Sometimes it works, but many times it does not. Lovebirds that do not like each other will fight, and they can fight to the death. Even if you do put two lovebirds together, you will need to have two individual cages to house them separately side-by-side until they get to know each other. After a period of time side-by-side, two lovebirds can be introduced to each other. At this point, they usually have an idea of how they feel about each other, and you’ll learn quickly whether they’ll be able to live in the same cage together or whether they’ll need to remain separated. Buying two lovebirds that don’t know each other already and expecting them to get along the same day in the same cage is unreasonable and dangerous. If you are not willing or able to have separate cages, introduce them slowly, and accept separate cages if they don’t get along, it’s best not to try a second bird in the first place.
Another thing to think about is the genders of the birds in question. Many pet owners do not know the genders of their lovebirds, especially youngsters. If a peachface and a fischer lovebird are housed in the same cage and they happen to be of the opposite sexes, then you are going to run into the issue of the pair attempting to breed. Peachface lovebirds should NOT be bred with fischer lovebirds, as this will create hybridized offspring that will be confused as adults. If you are not prepared to deal with the possibility of the birds attempting to breed, and you don’t know the genders of your lovebirds, then it is best not to house two in the same cage, regardless of their species. Raising babies is a time-consuming job that has many dangers. “Accidental” breeding or “letting nature take its course” is ridiculous and unfair to both the parent pair and the potential offspring. It should not be taken lightly. If you don’t want to research and put yourself into it fully, then DON’T let it happen.
Breeders should be better educated and more careful, not allowing the possibility of a peachface to pair off with a fischer. If it does happen, the birds should be separated and introduced to more appropriate mates.