Can stock exchange workers go on strike? Today, trade in the stock exchange of my country Israel (TASE) was cancelled due to a union dispute. So clearly, in Israel the answer to the question in the title is "yes". I can't say this comes as a surprise, as our country was founded on the bedrock of socialism, and those roots last until this day. But this is unfortunate as such disruptions surely concern foreign investors (and justly so).

However, I cannot imagine the same happening in the US, and indeed I couldn't find such an occurrence. Did I miss anything? Reading in Wikipedia, it looks like both NYSE and TASE are public (non-government) companies. So how come we see stock exchange strikes in Israel (this is not the first) and not in the US?

Is it because in the US there are multiple stock exchanges as opposed to Israel where TASE is a monopoly? Is it because unions in Israel are more powerful than in the US (and if so, how and why)? Perhaps US stock exchange workers are somehow classified as essential workers who aren't permitted to strike (e.g. by force of the Taylor Law)?
The Stock Exchange workers in US could strike if they wanted. The right to strike in US is enshrined in the US National Labor Relations Act of 1935. See also explanation of the law by the National Labor Relations Board  to see conditions under which strike can occur. None of the conditions seem to exclude stock exchange workers.

However, as @BrianRomanchuk points in his +1 comment, strikes are normally called by unions. According to the statistics published by U.S. Bureau of Labor Statistics in 2019 by occupation only $4.2\%$ workers were members of union and only $5.1\%$ represented by unions in the "Business and financial operations occupations" and if we look more narrowly only at finance as industry (which is arguably more appropriate for this question) the figures become $1.4\%$ and $2\%$. This being said I could not find any statistics specifically for only stock exchanges, but I would expect that unionization rates there would be lower than the aggregate for whole industry.

At the same time statistics show that people in the US working in finance and insurance industry were in 2018 ranked 4th in terms of average salary (see here). 

So to sum up, people in US working in financial industry are not generally members of unions or even represented by unions. This would presumably make organizing any meaningful strike difficult.  At the same time people working in finance industry in US are already in one of the highest paying professions meaning that there is most likely not much incentive to strike.