How to plot celestial equator in galactic coordinates? Why does my plot appear "backwards"?
Ok, community helped me to figure out that I faced the “mapping from the inside” issue (explained here). I'll use this answer to show my final code.
import numpy as np
from astropy.coordinates import SkyCoord
import astropy.units as u
import matplotlib.pyplot as plt
import seaborn as sns

sns.set()

def eq2gal(ra, dec):
    
    '''
    Transforms equatorial coordinates to galactic ones.
    Then prepares them for matplotlib aitoff projection. 
    '''
    
    eq = SkyCoord(ra, dec, unit=u.deg)
    gal = eq.galactic

    # Minus appears because of “mapping from the inside” issue
    l_gal, b_gal = -gal.l.wrap_at('180d').radian, gal.b.radian
    
    return l_gal, b_gal

def ecl2gal(lon_ecl, lat_ecl):
    
    '''
    Transforms ecliptic coordinates to galactic ones.
    Then prepares them for matplotlib aitoff projection.
    '''
    
    ecl = SkyCoord(lon_ecl, lat_ecl, unit=u.deg, frame='barycentricmeanecliptic')
    gal = ecl.transform_to('galactic')

    # Minus appears because of “mapping from the inside” issue
    l_gal, b_gal = -gal.l.wrap_at('180d').radian, gal.b.radian
    
    return l_gal, b_gal

# Equatorial plane
ra_all = np.linspace(-180, 180, 100)
dec_0 = np.zeros(100)

l_eq_gal, b_eq_gal = eq2gal(ra_all, dec_0)

# Ecliptic plane
lon_ecl = np.linspace(0, 360, 100)
lat_ecl = np.zeros(100)

l_ecl_gal, b_ecl_gal = ecl2gal(lon_ecl, lat_ecl)


plt.figure(figsize=(14,7))
plt.subplot(111, projection='aitoff')

plt.scatter(l_eq_gal, b_eq_gal, s=4, marker='v', label='Celestial Equator')
plt.scatter(l_ecl_gal, b_ecl_gal, s=4, marker='^', label='Eclptic')

# Essential thing is to rename RA axis ticks to transform them to conventional format
plt.xticks(ticks=np.radians([-150, -120, -90, -60, -30, 0, \
                             30, 60, 90, 120, 150]),
           labels=['150°', '120°', '90°', '60°', '30°', '0°', \
                   '330°', '300°', '270°', '240°', '210°'])


plt.grid(True)
plt.legend(fontsize=16, loc='lower center')

plt.title('Galactic', fontsize='16')

plt.show()