Support wise, I think any race will be interested in the success of the national team , and they would also play football regularly. However it different case when making football as a career, chinese is less inclined to play football professionally, opting for more "glamorous" profession. So to deduce the lack of chinese players in our national football scene is due to lack of support and interest, is not quite fair.
However I think this issue is not the main purpose of this thread. One can only wonder why a particular country's football team is not as good as their regional counterpart. For example, Poland is just next to Germany and their country's size isn't much different too (so we can assume talent pool is similar), but why is Germany so much better at football than Poland? Colombia and Argentina has similar population number, in fact Colombia 45m compared to 40m of argentina, but why if argentina were to play Colombia, more likely than not Argentina will be the better side?
Different education system at a young age? Different local league structure? Different administration system? Many factors.
I think one of the main factors would be how the young ones are being educated. In Malaysia, education system emphasizes on everyone learning the exact same thing and compete to the very limit to be at the top percentile. Straight 10,11 A1s is the target, so no wonder school would put more effort into getting more straight A students than to expand each student according to their individual talents (because for the school, the more straight a students, the more prestigious it is.
For a kid to be excellent at something other than education, the effort always comes from the parents, privately. Just as an example, a kid who grew up to be a great violin player is most likely due to their parents sending them to violin lessons which takes up a lot of time and money. So for world famous athletes like we have, for example Nicole David, I think the training she did while growing up is due to the great support of her family which involves private coaches, and less from the public education system. Now, which of our parents or authority figures, will be willing to spend money and time to send us to soccer training school? I mean they will probably say "if my son wants to play football, he can just join his friends at the park". Of course this is no offense to our parents, they have every intention of their kids to be successful. Just that majority family in Malaysia does not see football as the career to go and therefore do not put too much effort into that pathway.
We can talk about politics, wrong coaching system etc, but even if all these are perfect, these are not grassroot problem. If we as kids can't get good football training and education through public channels like schools, nor do we get a lot of investment from our own private department, then we more than likely will not reach the potential that we can achieve. Just imagine, if we have a kid just as talented as Messi, but through school he has to study real hard for exams, going to tuition during free time and besides that, parents asked him to train piano lessons on weekends, then one day he finish high school with view to study law because that's what the family "prefers" him to do.... There goes 1 talent.
Personally, I would like to talk about my brother. He is a Chinese boy, and when I started to play football at age 13, he was just 9. He would join me and the other boys my age to play every weekend, and he was a pretty good defender. I mean he has to defend against guys 3-4-5 years older than he is. He is more athletically built than me though

. When he was 11 or 12, he was picked to be wakil bahagian Bintulu (Sarawak) to compete against other towns and cities teams. He was the ONLY chinese boy in the team. However after that, he never continue actively play with school/town teams anymore, mainly to focus on studies I guess, as all his other friends are studying like hell too.
So as you can see:
1. Race is not an issue. if that person is really talented/work hard, and show great enthusiasm, he or she cannot be overlooked of that just because of race.
2. I can just wonder what would happen had in secondary school there are more systematic process and procedure in ensuring these young kids gets to expand their talent, and had my parents be more actively supportive of getting my brother to training school, more encouragement (they don't discourage, but they don't actively push us to play more either).
I'm now in Australia and they are starting to implement the grassroot system; big A-League teams are contributing money, coaching, training equipment etc to local city teams, if they have a kids team (for example, U11s). These U11 teams do have their own leagues and therefore this encourages more active support from their parents, with the aid of resources from the big clubs which makes their effort a bit more worthwhile.
This is not the only problem, but I don't think anyone can deny it is a major issue to look iin to if we want our national football status to be elevated, and be more consistent over a longer period of time.
Damn, tl;dr. Click spoiler at your own risk.