Not really, according to the CCES 2018 data. For each state, I've looked at the proportion of the voting population which identifies as a Republican (pid7)
and which also self-identifies as liberal (CC18_334A)
. Below are the results, plotted firstly as a proportion of the general voting population, and then as a proportion of the Republican population.
The top five states as a proportion of the voting population are Oklahoma (2.4%), Iowa (1.9%), Kentucky (1.6%), Hawaii (1.5%), and Rhode Island (1.4%). As a proportion of Republicans, the top five states are Rhode Island (6.8%), Hawaii (6.5%), Oklahoma (4.5%), Iowa (4.2%), and Connecticut (4.0%).

Data:
State,% of Voters,% of Republicans
RI,1.428,6.816
HI,1.531,6.482
OK,2.405,4.515
IA,1.854,4.159
CT,1.232,3.963
NM,1.137,3.959
IL,1.336,3.568
GA,1.414,3.200
KY,1.551,2.903
ME,0.979,2.862
PA,1.070,2.442
ND,1.241,2.361
CA,0.651,2.258
NY,0.642,2.214
MI,0.826,2.123
MN,0.821,2.104
WV,0.965,2.096
NE,1.103,2.047
IN,0.918,1.835
NC,0.779,1.835
FL,0.773,1.811
OR,0.709,1.787
NV,0.639,1.697
TX,0.742,1.670
WI,0.729,1.583
CO,0.565,1.456
ID,0.799,1.388
MD,0.411,1.325
OH,0.583,1.268
TN,0.665,1.258
AL,0.603,1.230
NJ,0.398,1.158
SD,0.734,1.123
UT,0.575,1.050
AR,0.540,1.027
MS,0.491,1.004
NH,0.403,0.985
MA,0.223,0.905
VT,0.296,0.893
WA,0.334,0.890
VA,0.292,0.763
WY,0.537,0.723
LA,0.266,0.618
MO,0.247,0.509
KS,0.222,0.458
AZ,0.197,0.446
SC,0.103,0.216
AK,0.000,0.000
DE,0.000,0.000
DC,0.000,0.000
MT,0.000,0.000