Hair thinning from scalp psoriasis and will it be an issue to use finasteride?

I suggest you start in office prp/acell treatments and at home theradome which will help your psoriasis too (see link).

You need a formal evaluation to see what type of hair loss you may have. when you have hairless its best to do a full hormonal workup for internal optimization plus scalp biopsies or scrapings to rule out any stress related, inflammatory, autoimmune or infectious causes of hair loss. In general most people with early hair loss have telogen (stress related) and/or androgenetic (normal aging) and both can be treated with in office treatments like steroid injections, PRP/acell, Exosomes and at home treatments like oral medications, oral vitamins like Viviscal, topical exfoliating sprays like Restorsea, and weekly growth factors like anteagemd. See an expert for an evaluation. If hair loss is significant it may requires hair transplant (follicular unit translation).