The rules on Inspiration, from the Basic Rules state:

Typically, DMs award it when you play out your personality traits, give in to the drawbacks presented by a flaw or bond, and otherwise portray your character in a compelling way.

If you choose unwisely, giving into drawbacks, this could potentially lead to the detriment of your fun or someone else's fun.

Does awarding Inspiration for this kind of behavior cause issues with My Guy Syndrome among players?

Please support your answers with evidence from actual experience.

No, not when used properly.

DM has control over what inspiration encourages

The key thing here is that the DM controls when inspiration is awarded. As a DM, I give it freely and often and have never had a case of My Guy Syndrome (MGS) come specifically from this mechanic. In fact, I use it (successfully) as a way to reward players for non-MGS behaviors (behaviors the group as a whole find fun).

It could be used to create a worse problem though if you encourage the wrong things. In this case, you can make an MGS issue worse if you keep rewarding actions that are negatively affecting group fun in the name of good character RP. However, I think inspiration can only amplify a problem that already exists.

I sincerely doubt, and have never observed, that inspiration as a mechanic is powerful enough to actually cause MGS behaviors to appear outside of any other factors. And, on the flip side, when I have had problems with MGS at my table, inspiration has never been enough to fix it (and also runs afoul of my policy to fix out-of-game issues with out-of-game solutions as a first step).

My Guy Syndrome vs. Roleplaying

You seem to be conflating two things: role-playing and My Guy Syndrome. Role-playing often involves having a character have some sort of flaws or acting out drawbacks related to their personality or backstory. That's all part of storytelling. If every character was perfect and unflawed, stories about characters overcoming those flaws or developing as a character cease to exist. This is the kind of thing this passage is providing a mechanic to encourage.

On the other hand, My Guy Syndrome is what happens when you role-play any part of your character in a way that negatively affects your table's enjoyment and fun and then justify it as the only way you can act because it is what your character would do and that you have no choice but to do this.

If you are acting out a character flaw, and there is no issue with how much fun it is at the table and is not causing any other issues, then there is no problem and thus no MGS.

Other parts of the book provide more guidance that should be used with this

MGS is something that only occurs when a player is roleplaying as their character problematically. Anything that encourages more roleplaying without explicitly telling the player not to do so could be construed as "encouraging" MGS. However, the rules must be read in context. The portion that you read is in the DM's guidance for inspiration. In the PHB it says:

When another player character does something that really contributes to the story in a fun and interesting way, you can give up your inspiration to give that character inspiration.

Not the emphasis on group fun and story? That is pushing the players away from MGS. Taking one section of one part of the DM's manual without any of the other guidance the books offer on the matter is bound to give a skewed view of the guidance it offers. As with most things: context matters.

No

There is a difference between being a "my guy" and roleplaying well and within the constraints of what your table considers 'fun' and 'engaging.'

You can play a roleplay character without being that guy.

DM may not reward "my guy" actions

As inspiration is a DM thing to hand out, they are in total control of what type of behavior they want to reward. If you're heading into My Guy territory, you're likely going to be talked to and not rewarded.

If a DM feels that roleplaying is heading into My Guy territory and others at the table aren't having fun, there is no requirement for them to hand out Inspiration for it - and they can discuss such potential issues with that player if they feel like they should.

DMs can and should provide inspiration for roleplay of flaws/bonds or other traits or builds that make it enjoyable for the player and their tablemates. And that can be done without venturing into My Guy Syndrome territory.

How I treat inspiration - suboptimal isn't always MGS

When I DM, I do my best to provide inspiration to those who do fun/interesting/clever things with their character. That can be through combat actions, through roleplaying their traits, and it may be doing so with optimal or sub optimal strategies. It's whatever added to the table experience positively. It doesn't always happen, but I try to be open and fair about when//how I'll do it and what I'm looking for.

What I'm not looking to do is promote actions that take away from the fun of the table. My Guy Syndrome does that for me as a DM, so I would actively discourage this by not providing inspiration and by discussing table antics like that with the player to help them improve and work with them to figure out positive ways in which they can 'be' their character.

No

My Guy Syndrome is what happens when a player plays to their character no matter what, even if it means that other players aren't having fun. It means that the player does not take responsibility for the character's actions, and instead uses the character's personality as an excuse.

The main thing here is that My Guy Syndrome isn't fun for the other players.

It is perfectly feasible to play a flawed or not-entirely-cooperative character in a way that other players still have fun in spite of (or maybe have even more fun because of) it, so playing to a character's flaws or bonds is not necessarily My Guy Syndrome.

Remember, a flawed character can still be a fun character, both for that character's player, and for the other players in the group! As long as those flaws and bonds aren't such that they'll stop people from having fun, playing to them isn't My Guy Syndrome!

No, because the DM doesn't reward disruptive activity.

Good answers to this question already, but let me phrase it this way:

The key difference between Inspiration and My Guy Syndrome is that receiving Inspiration is an extrinsic motivator which rewards what the DM considers good play.

Flaws like those of the Criminal background can indeed validate a player character who puts personal gain before party, but the player who acts this way is usually doing so out of an intrinsic motivation: personal gain (I'm stealing the magic boots because I want my guy to become stronger), fun (I find pranking the other players amusing) a sense of authenticity (I enjoy playing the villain), and so on.

But those players will do that even if you don't reward it. Players have been pulling "that's what my guy would do" as an excuse since long before Flaws and Background appeared in the games. The DM traditionally doesn't decide a player character's personality or actions, so players hold most of the power here.

Conversely, the Inspiration mechanic is purely up to the DM, and rewarding players for playing their character's negative traits isn't mandatory. In fact, it's the opposite: you can reward the rogue with Inspiration for not stealing from the party (hey, it's character development!) and openly refuse to give Inspiration when they do misbehave.

Inspiration therefore creates a situation in which the player is still free to invoke the Wangrod Defense ("it's what my guy would do"), but they are openly rewarded for choosing the more amicable alternative.