Am I required to have anti-collision lights on my homebuilt?
No, if you are only going to using your aircraft for day, VFR flight. FAR 91.205 lists the instrument and equipment requirements for standard category aircraft. This FAR does not apply to Experimental-Amateur Built aircraft.
If you intend to use your aircraft for either night VFR or IFR flight, you will have to comply with the requirements of FAR 91.205 because the operating limitations you receive as a part of your airworthiness certificate will include the following language:
“After completion of phase I flight testing, unless appropriately equipped for night and/or instrument flight in accordance with § 91.205, this aircraft is to be operated under VFR, day only.”