Matplotlib: setting x-limits also forces tick labels?

The additional ticklabels that overlap originate from some minor ticklabels, which are present in the plot. To get rid of them, one can set the minor formatter to the NullFormatter:

plt.gca().xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())

The complete code from the question might then look like

import matplotlib.pyplot as plt
import matplotlib.ticker
import numpy as np

x = np.linspace(0,2.5)
y = np.sin(x*6)
plt.plot(x,y, '--', color="k", zorder=1, lw=2)

plt.xlim(0.4,2.0)

plt.xscale('log')

xticks = [0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0]
ticklabels = ['0.4', '0.6', '0.8', '1.0', '1.2', '1.4', '1.6', '1.8', '2.0']
plt.xticks(xticks, ticklabels)

plt.gca().xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())

plt.show()

A code that may be more intuitive as it is not setting the xticklabels as strings would be the following, where we use a FixedLocator and a ScalarFormatter.
This code produces the identical plot as the above.

import matplotlib.pyplot as plt
import matplotlib.ticker
import numpy as np

x = np.linspace(0,2.5)
y = np.sin(x*6)
plt.plot(x,y, '--', color="k", zorder=1, lw=2)

plt.xlim(0.4,2.0)
plt.xscale('log')

xticks = [0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0]

xmajorLocator = matplotlib.ticker.FixedLocator(locs=xticks) 
xmajorFormatter = matplotlib.ticker.ScalarFormatter()
plt.gca().xaxis.set_major_locator( xmajorLocator )
plt.gca().xaxis.set_major_formatter( xmajorFormatter )
plt.gca().xaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())

plt.show()