As MMario said , If you are getting paid , you do what you are getting paid to sing , the rest of the time you do what YOU want to do . When i first started singing , I didnt play any thing I could sing with ( I am an Ex Jazz Clarinet and Sax player) so did Unaccompanied songs and played whistle tunes . Then I realised I wanted to sing a lot of contemporary songs (Leon Rosselsson and such)
so I learnt guitar ,then banjo when I briefly teamed up with another guitarist . I now work pro , mostly playing mandolin and whistle ,
with occasioanl bits of guitar and banjo , and still sing the odd 'Trad' unaccompanied song . When i drop in on my local clubs i am often told I should sing more unaccomp songs , and that ISNT because I am a crap instrumentalist , but I dont do as many as I could . They ARE a useful fallback if I break a string , or have a tuning problem and dont want to waste time .
I find that an accompanied song has to be well worked in as an arrangement before I feel comfortable with it , whereas a Trad song is a lot easier to get up to speed . Just keep at it and enjoy the music !