ValueError: Shapes (None, 1) and (None, 2) are incompatible

You can change the labels from binary values to categorical and continue with the same code. For example,

from keras.utils import to_categorical
one_hot_label = to_cateorical(input_labels)
# change to [1, 0, 0,..., 0]  --> [[0, 1], [1, 0], ..., [1, 0]]

You can go through this link to understand better Keras API.

If you want to use categorical crossentropy for two classes, use softmax and do one hot encoding. Either for binary classification, you can use binary crossentropy as in previous answer mentioned by using sigmoid activation function.

1. Categorical Cross entropy:

model = Sequential([
    Conv2D(32,3, activation='relu', input_shape=(48,48,1)),
    BatchNormalization(),
    MaxPooling2D(pool_size=(3, 3)),

    Flatten(),
    Dense(512, activation='relu'),
    Dense(2,activation='softmax')  # activation change
])
model.compile(optimizer='adam',
              loss='categorical_crossentropy', # Loss
              metrics=['accuracy'])

2. Binary Crossentropy

model = Sequential([
    Conv2D(32,3, activation='relu', input_shape=(48,48,1)),
    BatchNormalization(),
    MaxPooling2D(pool_size=(3, 3)),

    Flatten(),
    Dense(512, activation='relu'),
    Dense(1,activation='sigmoid') #activation change
])
model.compile(optimizer='adam',
              loss='binary_crossentropy', # Loss
              metrics=['accuracy'])

If your dataset was load with image_dataset_from_directory, use label_mode='categorical'

train_ds = tf.keras.preprocessing.image_dataset_from_directory(
  path,
  label_mode='categorical'
)

Or load with flow_from_directory, flow_from_dataframe then use class_mode='categorical'

train_ds = ImageDataGenerator.flow_from_directory(
  path,
  class_mode='categorical'
)

i was facing the same problem my shapes were

shape of X (271, 64, 64, 3)
shape of y (271,)
shape of trainX (203, 64, 64, 3)
shape of trainY (203, 1)
shape of testX (68, 64, 64, 3)
shape of testY (68, 1)

and

loss="categorical_crossentropy"

i changed it to

loss="sparse_categorical_crossentropy"

and it worked like a charm for me

Change Categorical Cross Entropy to Binary Cross Entropy since your output label is binary. Also Change Softmax to Sigmoid since Sigmoid is the proper activation function for binary data