TLDR: Choose a print shop that provides ICC profiles.

Soft proofing is an important step for optimal results. If a shop doesn't share its profiles there are two reasons that come to my mind: lack of knowledge (very bad), or different printer types for the same printing product, meaning multiple orders could give different results even with the same picture.

Consider that every piece in the chain from lens to print deals differently with colors. This is defined by engineering and limited in accuracy by technology (e.g., types of colors a printer uses), production tolerances and physics. Therefore color profiles exist for cameras, displays and printers. This allows you to see the limits of reproduction in a given medium, which is usually done by soft-proofing. A print shops that apparently skimps on color management breaks this chain. If a photographer wants to publish his art as he envisioned it and not just snapshots, it's advisable to look for print shops that provide ICC profiles.

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What to do if the print shop requests files in a specific color space?

If you decide to go with this shop, adhere to the selection.
A known error is to send pictures with a CMYK color space such as offset printers use, while most shops expect some form of RGB color space. Often a shop will accept multiple formats (sRGB, Adobe RGB, ProPhoto RGB). sRGB is the smallest of the color spaces listed, thus its coverage of the color space the printer is capable of is the smallest. On the other hand, an sRGB jpeg with 8 bits per color channel will have finer color steps than a ProPhoto RGB with 8 bits per color channel.