Can online activism hurt my employability?
Absolutely. But it's largely impossible to predict to what extent. Public activism, whether online or not, can negatively affect your profile as a job candidate. Supporting a controversial topic (such as NAMBLA) would get you rejected from most jobs. Supporting movements with controversial methods (like Antifa) would likewise reflect negatively on you. More broadly, employers might wonder if you're so politically active that it will impact your ability to do your job (or work overtime) or if you'll bring that kind of activism to work with you (by trying to recruit colleagues). And sometimes an employer may simply disagree with your political stance which could cause both conscious or subconscious bias.
Your political activism will simply be another data point that a hiring manager gets to consider. Some will think it's net negative, some will think it's positive. You may lose out on certain jobs that you'd otherwise have been offered and you may find contacts or get offers that you wouldn't have gotten without being publicly active. Most hiring managers won't find out about your activism or won't consider it important.
Generally speaking, if your employment opportunities are few, I would encourage you to err on the side of caution and limit your public activism. But if you have an in-demand profile and if you aren't worried about potentially increasing the time your future job searches could take, there's no reason not to be publicly politically active.
It should also be said that the country and industry you're in does matter when it comes to this. Most "Western" countries and most modern industries (like web development) have grown considerably more progressive and tend to respect the private nature of an employee's off-work activities. Employee protection laws also help in that regard.
Finally, keep in mind that not every hiring manager will be googling his candidates. You should be aware that some do and that your colleagues can also look you up so you want to make sure your online profile is relatively clean, but it's unlikely to come up in every job application.