抜きにして / 抜きで【ぬきにして / ぬきで】

抜きで and 抜きにして go after a noun and mean "without it": the noun is something that would normally be there, and you leave it out. 抜きで is the everyday form for leaving out a thing – an ingredient, a meal, a person.

Before another noun it takes の: さとう砂糖ぬき抜きのこうひいコーヒー, coffee without sugar.

抜きで or 抜きにして

抜きにして sets aside something abstract – formalities, jokes, small talk – so you can get to the point. The noun usually takes は, the phrase opens the sentence, and it sounds a little more formal than 抜きで.

The line is loose. おせじお世辞ぬき抜きで "without flattery" is as natural as お世辞は抜きにして. And as the verb at the end of a sentence, ぬき抜きにする just means "leave out", so a request about food can take it too.

Cannot do without: 抜きには

Followed by は and a negative, ぬき抜きには, ぬき抜きにしては or ぬき抜きでは says the noun is indispensable: without it, the thing does not happen. The second half is a negative, or a "would not have" about the past.