Are all Stratocaster Standard guitar pickups compatible? Want to remove my Squire Strat pickups and install Rails Seymour Duncan in the bridge, HS-4 DiMarzio in the middle and SD Jr.59 (PAF) in the neck. Will they work together without changing the other electronics? Thank you.
You don't have to change the other electronics, although you might find that the volume and tone knobs don't exactly respond the way they used to. They are compatible but can vary, so you can change out the other electronics if you want to in order to get a different sound or control behavior, but it's personal preference.
In terms of how the three pickups will interact, that's also a matter of taste and they might sound the way you want just as they are, or you might not like how they combine. If you don't like the combinations, there's not a huge amount of electronics to try changing in a Strat. You can change the pickup selector wiring so you are combining different pairs of pickups in the "in between" positions. You can also reverse the polarity of one of the pickups so that it combines differently with the others. Changing the capacitors or the pots might change the tones you have available, but probably won't do as much regarding how the pickups combine, unless you really wire things differently and make them each dedicated volume knobs for each pickup or something radical like that.
Caveats when changing Strat-style pickups include having compatible pickup covers, screws, and springs. If the new pickups do not need covers or come with covers, you're fine. The covers on your current pickups might not fit the new ones. The same is possible with the screws, and possible but less likely with the springs. If you buy pickups new in box and they are meant to go into a Strat, they should include the correct parts so you don't have to scramble to make something work.