I make homemade laundry soap I found the recipe online, and it uses name brand products, would I be able to sell this?

Yes, providing the recipe meets regulatory codes governing sale of this type of product- but be careful not to use the "name brand(s)" to mark your product. You might list the ingredients in small print, but make sure to do so in a manner that will avoid any likelihood of confusing your product with its name brand ingredients.

I don't see any IP issues that would stop you unless you used the brand names in your marketing.

Yes. The fact that you purchase the "brand name products" gives you the right to use them as you choose - and that includes combining them and selling the new laundry soap product. However, you cannot use the NAMES of the brand name products as your list of ingredients - as those names are likely registered trademarks for each of the products that you have combined.