See this related question - it's about the video production's vibe that Sony Vegas in "unprofessional" compared to Avid (who make ProTools) and Final Cut.
Let's start with this: FLStudio it's a tool with which you're familiar. That's a huge plus in terms of learning curve for getting things done.
With DAWs, the output is comparable. ProTools can't make better ones or zeros than any other package. There are going to be inherent differences in the audio codecs depending on which one ships with whose products.
The tool, in and of itself, it not the issue. Professionalism comes from a.) the recording quality and b.) the skill of the engineer. Record with a crappy mic that's not been properly placed in a room that's not properly soundproofed, and Bob Katz himself couldn't fix it. Conversely, mic it right and choose the right place to record, and if you know your tool, you can create awesome recordings.
Should you switch? That's up to you, but here are some things to consider:
1.) Can you accomplish everything you need to record and output great audio with FLStudio?
2.) Will you ever have a need to exchange files with someone else...e.g., will you ever need to send your stubs to a mastering studio? And is the output you send them compatible with, most likely, ProTools or Live?
3.) How important is it that it's compatible with other studios' equipment?
4.) Can FLStudio output redbook compliant CD image files?
5.) How important is it that you have an image of professionalism? Will you lose business because of your software? or will you retain business, regardless of software because of your mad audio skillz?
If you know how to make great audio, that's where the professionalism comes from. Not the software. Yes, there may be solid business reasons to invest in one package or another, mostly revolving around the extent to which you'll share files to collaborate. Secondary will be for marketing purposes...but honestly, with some great demos, you can overcome the second quite handily.
Software is nothing more than a tool. If I can make true cuts in a piece of wood with a Craftsman saw, it doesn't matter that the saw isn't Black and Decker. If it does what you need and you're happy with the results, phtphptpht to the naysayers. :)