You can translate each errorbar by adding the default data transform to a prior translation in data space. This is possible when knowing that categories are in general one data unit away from each other.
import numpy as np; np.random.seed(42)
import matplotlib.pyplot as plt
from matplotlib.transforms import Affine2D
x = list("ABCDEF")
y1, y2 = np.random.randn(2, len(x))
yerr1, yerr2 = np.random.rand(2, len(x))*4+0.3
fig, ax = plt.subplots()
trans1 = Affine2D().translate(-0.1, 0.0) + ax.transData
trans2 = Affine2D().translate(+0.1, 0.0) + ax.transData
er1 = ax.errorbar(x, y1, yerr=yerr1, marker="o", linestyle="none", transform=trans1)
er2 = ax.errorbar(x, y2, yerr=yerr2, marker="o", linestyle="none", transform=trans2)
plt.show()

Alternatively, you could translate the errorbars after applying the data transform and hence move them in units of points.
import numpy as np; np.random.seed(42)
import matplotlib.pyplot as plt
from matplotlib.transforms import ScaledTranslation
x = list("ABCDEF")
y1, y2 = np.random.randn(2, len(x))
yerr1, yerr2 = np.random.rand(2, len(x))*4+0.3
fig, ax = plt.subplots()
trans1 = ax.transData + ScaledTranslation(-5/72, 0, fig.dpi_scale_trans)
trans2 = ax.transData + ScaledTranslation(+5/72, 0, fig.dpi_scale_trans)
er1 = ax.errorbar(x, y1, yerr=yerr1, marker="o", linestyle="none", transform=trans1)
er2 = ax.errorbar(x, y2, yerr=yerr2, marker="o", linestyle="none", transform=trans2)
plt.show()

While results look similar in both cases, they are fundamentally different. You will observe this difference when interactively zooming the axes or changing the figure size.